Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(157,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 8, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.n (of order \(5\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{5})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 157.9 | ||
Character | \(\chi\) | \(=\) | 429.157 |
Dual form | 429.2.n.d.235.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{4}{5}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.25286 | − | 1.63680i | 1.59301 | − | 1.15739i | 0.693534 | − | 0.720424i | \(-0.256053\pi\) |
0.899478 | − | 0.436967i | \(-0.143947\pi\) | |||||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | 1.77823 | − | 5.47283i | 0.889116 | − | 2.73642i | ||||
\(5\) | 2.25719 | + | 1.63994i | 1.00945 | + | 0.733405i | 0.964093 | − | 0.265566i | \(-0.0855587\pi\) |
0.0453532 | + | 0.998971i | \(0.485559\pi\) | |||||||
\(6\) | 2.25286 | + | 1.63680i | 0.919726 | + | 0.668220i | ||||
\(7\) | −1.26682 | + | 3.89888i | −0.478815 | + | 1.47364i | 0.361929 | + | 0.932206i | \(0.382118\pi\) |
−0.840743 | + | 0.541434i | \(0.817882\pi\) | |||||||
\(8\) | −3.23079 | − | 9.94334i | −1.14226 | − | 3.51550i | ||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 7.76939 | 2.45690 | ||||||||
\(11\) | −1.80345 | − | 2.78345i | −0.543760 | − | 0.839241i | ||||
\(12\) | 5.75448 | 1.66118 | ||||||||
\(13\) | 0.809017 | − | 0.587785i | 0.224381 | − | 0.163022i | ||||
\(14\) | 3.52771 | + | 10.8572i | 0.942820 | + | 2.90170i | ||||
\(15\) | −0.862170 | + | 2.65349i | −0.222611 | + | 0.685127i | ||||
\(16\) | −14.2428 | − | 10.3480i | −3.56070 | − | 2.58700i | ||||
\(17\) | 0.435067 | + | 0.316095i | 0.105519 | + | 0.0766642i | 0.639294 | − | 0.768963i | \(-0.279227\pi\) |
−0.533774 | + | 0.845627i | \(0.679227\pi\) | |||||||
\(18\) | −0.860515 | + | 2.64839i | −0.202825 | + | 0.624233i | ||||
\(19\) | −0.145719 | − | 0.448476i | −0.0334302 | − | 0.102887i | 0.932949 | − | 0.360008i | \(-0.117226\pi\) |
−0.966379 | + | 0.257121i | \(0.917226\pi\) | |||||||
\(20\) | 12.9890 | − | 9.43703i | 2.90442 | − | 2.11018i | ||||
\(21\) | −4.09953 | −0.894591 | ||||||||
\(22\) | −8.61885 | − | 3.31883i | −1.83755 | − | 0.707578i | ||||
\(23\) | −7.04636 | −1.46927 | −0.734634 | − | 0.678464i | \(-0.762646\pi\) | ||||
−0.734634 | + | 0.678464i | \(0.762646\pi\) | |||||||
\(24\) | 8.45831 | − | 6.14532i | 1.72655 | − | 1.25441i | ||||
\(25\) | 0.860404 | + | 2.64805i | 0.172081 | + | 0.529610i | ||||
\(26\) | 0.860515 | − | 2.64839i | 0.168761 | − | 0.519393i | ||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | 19.0852 | + | 13.8662i | 3.60677 | + | 2.62047i | ||||
\(29\) | −0.836115 | + | 2.57330i | −0.155263 | + | 0.477849i | −0.998187 | − | 0.0601822i | \(-0.980832\pi\) |
0.842925 | + | 0.538031i | \(0.180832\pi\) | |||||||
\(30\) | 2.40087 | + | 7.38913i | 0.438337 | + | 1.34906i | ||||
\(31\) | −0.649155 | + | 0.471638i | −0.116592 | + | 0.0847088i | −0.644553 | − | 0.764560i | \(-0.722957\pi\) |
0.527961 | + | 0.849268i | \(0.322957\pi\) | |||||||
\(32\) | −28.1145 | −4.96999 | ||||||||
\(33\) | 2.08992 | − | 2.57531i | 0.363808 | − | 0.448304i | ||||
\(34\) | 1.49753 | 0.256824 | ||||||||
\(35\) | −9.25342 | + | 6.72300i | −1.56411 | + | 1.13639i | ||||
\(36\) | 1.77823 | + | 5.47283i | 0.296372 | + | 0.912139i | ||||
\(37\) | −0.0991861 | + | 0.305263i | −0.0163061 | + | 0.0501850i | −0.958878 | − | 0.283817i | \(-0.908399\pi\) |
0.942572 | + | 0.334002i | \(0.108399\pi\) | |||||||
\(38\) | −1.06235 | − | 0.771841i | −0.172336 | − | 0.125209i | ||||
\(39\) | 0.809017 | + | 0.587785i | 0.129546 | + | 0.0941210i | ||||
\(40\) | 9.01403 | − | 27.7423i | 1.42524 | − | 4.38645i | ||||
\(41\) | 1.02420 | + | 3.15218i | 0.159954 | + | 0.492288i | 0.998629 | − | 0.0523444i | \(-0.0166693\pi\) |
−0.838675 | + | 0.544632i | \(0.816669\pi\) | |||||||
\(42\) | −9.23566 | + | 6.71010i | −1.42509 | + | 1.03539i | ||||
\(43\) | 3.75472 | 0.572590 | 0.286295 | − | 0.958142i | \(-0.407576\pi\) | ||||
0.286295 | + | 0.958142i | \(0.407576\pi\) | |||||||
\(44\) | −18.4403 | + | 4.92036i | −2.77998 | + | 0.741771i | ||||
\(45\) | −2.79004 | −0.415915 | ||||||||
\(46\) | −15.8744 | + | 11.5335i | −2.34056 | + | 1.70052i | ||||
\(47\) | −1.87974 | − | 5.78524i | −0.274188 | − | 0.843864i | −0.989433 | − | 0.144990i | \(-0.953685\pi\) |
0.715245 | − | 0.698874i | \(-0.246315\pi\) | |||||||
\(48\) | 5.44027 | − | 16.7434i | 0.785235 | − | 2.41670i | ||||
\(49\) | −7.93333 | − | 5.76390i | −1.13333 | − | 0.823415i | ||||
\(50\) | 6.27269 | + | 4.55738i | 0.887092 | + | 0.644510i | ||||
\(51\) | −0.166181 | + | 0.511452i | −0.0232700 | + | 0.0716176i | ||||
\(52\) | −1.77823 | − | 5.47283i | −0.246596 | − | 0.758946i | ||||
\(53\) | 10.3763 | − | 7.53879i | 1.42529 | − | 1.03553i | 0.434419 | − | 0.900711i | \(-0.356954\pi\) |
0.990870 | − | 0.134822i | \(-0.0430461\pi\) | |||||||
\(54\) | −2.78469 | −0.378948 | ||||||||
\(55\) | 0.493976 | − | 9.24032i | 0.0666076 | − | 1.24596i | ||||
\(56\) | 42.8608 | 5.72751 | ||||||||
\(57\) | 0.381496 | − | 0.277173i | 0.0505304 | − | 0.0367125i | ||||
\(58\) | 2.32832 | + | 7.16582i | 0.305723 | + | 0.940919i | ||||
\(59\) | 0.00194626 | − | 0.00598998i | 0.000253382 | − | 0.000779828i | −0.950930 | − | 0.309407i | \(-0.899869\pi\) |
0.951183 | + | 0.308627i | \(0.0998695\pi\) | |||||||
\(60\) | 12.9890 | + | 9.43703i | 1.67687 | + | 1.21831i | ||||
\(61\) | 7.97731 | + | 5.79586i | 1.02139 | + | 0.742084i | 0.966567 | − | 0.256412i | \(-0.0825405\pi\) |
0.0548230 | + | 0.998496i | \(0.482541\pi\) | |||||||
\(62\) | −0.690477 | + | 2.12507i | −0.0876907 | + | 0.269884i | ||||
\(63\) | −1.26682 | − | 3.89888i | −0.159605 | − | 0.491213i | ||||
\(64\) | −34.8524 | + | 25.3218i | −4.35655 | + | 3.16522i | ||||
\(65\) | 2.79004 | 0.346062 | ||||||||
\(66\) | 0.493028 | − | 9.22259i | 0.0606875 | − | 1.13522i | ||||
\(67\) | −4.14523 | −0.506420 | −0.253210 | − | 0.967411i | \(-0.581486\pi\) | ||||
−0.253210 | + | 0.967411i | \(0.581486\pi\) | |||||||
\(68\) | 2.50358 | − | 1.81896i | 0.303604 | − | 0.220581i | ||||
\(69\) | −2.17744 | − | 6.70148i | −0.262133 | − | 0.806764i | ||||
\(70\) | −9.84245 | + | 30.2919i | −1.17640 | + | 3.62058i | ||||
\(71\) | 11.8848 | + | 8.63482i | 1.41047 | + | 1.02476i | 0.993254 | + | 0.115955i | \(0.0369930\pi\) |
0.417213 | + | 0.908809i | \(0.363007\pi\) | |||||||
\(72\) | 8.45831 | + | 6.14532i | 0.996822 | + | 0.724233i | ||||
\(73\) | −4.36333 | + | 13.4289i | −0.510689 | + | 1.57174i | 0.280302 | + | 0.959912i | \(0.409565\pi\) |
−0.790991 | + | 0.611827i | \(0.790435\pi\) | |||||||
\(74\) | 0.276202 | + | 0.850063i | 0.0321079 | + | 0.0988178i | ||||
\(75\) | −2.25257 | + | 1.63658i | −0.260104 | + | 0.188977i | ||||
\(76\) | −2.71356 | −0.311266 | ||||||||
\(77\) | 13.1370 | − | 3.50529i | 1.49710 | − | 0.399465i | ||||
\(78\) | 2.78469 | 0.315304 | ||||||||
\(79\) | 0.867738 | − | 0.630449i | 0.0976282 | − | 0.0709310i | −0.537900 | − | 0.843009i | \(-0.680782\pi\) |
0.635528 | + | 0.772077i | \(0.280782\pi\) | |||||||
\(80\) | −15.1786 | − | 46.7148i | −1.69701 | − | 5.22287i | ||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 7.46687 | + | 5.42500i | 0.824578 | + | 0.599091i | ||||
\(83\) | −1.42551 | − | 1.03570i | −0.156470 | − | 0.113682i | 0.506795 | − | 0.862066i | \(-0.330830\pi\) |
−0.663266 | + | 0.748384i | \(0.730830\pi\) | |||||||
\(84\) | −7.28991 | + | 22.4360i | −0.795395 | + | 2.44797i | ||||
\(85\) | 0.463651 | + | 1.42697i | 0.0502900 | + | 0.154777i | ||||
\(86\) | 8.45886 | − | 6.14572i | 0.912142 | − | 0.662710i | ||||
\(87\) | −2.70572 | −0.290084 | ||||||||
\(88\) | −21.8502 | + | 26.9250i | −2.32924 | + | 2.87022i | ||||
\(89\) | 6.15187 | 0.652097 | 0.326049 | − | 0.945353i | \(-0.394283\pi\) | ||||
0.326049 | + | 0.945353i | \(0.394283\pi\) | |||||||
\(90\) | −6.28557 | + | 4.56673i | −0.662557 | + | 0.481376i | ||||
\(91\) | 1.26682 | + | 3.89888i | 0.132799 | + | 0.408714i | ||||
\(92\) | −12.5301 | + | 38.5636i | −1.30635 | + | 4.02053i | ||||
\(93\) | −0.649155 | − | 0.471638i | −0.0673142 | − | 0.0489066i | ||||
\(94\) | −13.7041 | − | 9.95658i | −1.41347 | − | 1.02694i | ||||
\(95\) | 0.406561 | − | 1.25127i | 0.0417123 | − | 0.128377i | ||||
\(96\) | −8.68786 | − | 26.7385i | −0.886701 | − | 2.72899i | ||||
\(97\) | −2.92823 | + | 2.12748i | −0.297317 | + | 0.216013i | −0.726435 | − | 0.687235i | \(-0.758824\pi\) |
0.429118 | + | 0.903248i | \(0.358824\pi\) | |||||||
\(98\) | −27.3070 | −2.75843 | ||||||||
\(99\) | 3.09509 | + | 1.19182i | 0.311068 | + | 0.119782i | ||||
\(100\) | 16.0223 | 1.60223 | ||||||||
\(101\) | 10.5617 | − | 7.67352i | 1.05093 | − | 0.763544i | 0.0785396 | − | 0.996911i | \(-0.474974\pi\) |
0.972389 | + | 0.233367i | \(0.0749743\pi\) | |||||||
\(102\) | 0.462762 | + | 1.42423i | 0.0458202 | + | 0.141020i | ||||
\(103\) | −0.857268 | + | 2.63840i | −0.0844691 | + | 0.259969i | −0.984366 | − | 0.176133i | \(-0.943641\pi\) |
0.899897 | + | 0.436102i | \(0.143641\pi\) | |||||||
\(104\) | −8.45831 | − | 6.14532i | −0.829406 | − | 0.602598i | ||||
\(105\) | −9.25342 | − | 6.72300i | −0.903041 | − | 0.656098i | ||||
\(106\) | 11.0368 | − | 33.9677i | 1.07199 | − | 3.29923i | ||||
\(107\) | −1.76051 | − | 5.41829i | −0.170195 | − | 0.523806i | 0.829187 | − | 0.558972i | \(-0.188804\pi\) |
−0.999381 | + | 0.0351657i | \(0.988804\pi\) | |||||||
\(108\) | −4.65547 | + | 3.38240i | −0.447973 | + | 0.325471i | ||||
\(109\) | 0.283223 | 0.0271279 | 0.0135639 | − | 0.999908i | \(-0.495682\pi\) | ||||
0.0135639 | + | 0.999908i | \(0.495682\pi\) | |||||||
\(110\) | −14.0117 | − | 21.6257i | −1.33596 | − | 2.06193i | ||||
\(111\) | −0.320973 | −0.0304654 | ||||||||
\(112\) | 58.3888 | − | 42.4219i | 5.51722 | − | 4.00850i | ||||
\(113\) | 0.171959 | + | 0.529235i | 0.0161765 | + | 0.0497863i | 0.958819 | − | 0.284018i | \(-0.0916675\pi\) |
−0.942642 | + | 0.333804i | \(0.891668\pi\) | |||||||
\(114\) | 0.405781 | − | 1.24886i | 0.0380049 | − | 0.116967i | ||||
\(115\) | −15.9050 | − | 11.5556i | −1.48315 | − | 1.07757i | ||||
\(116\) | 12.5964 | + | 9.15183i | 1.16955 | + | 0.849727i | ||||
\(117\) | −0.309017 | + | 0.951057i | −0.0285686 | + | 0.0879252i | ||||
\(118\) | −0.00541973 | − | 0.0166802i | −0.000498926 | − | 0.00153554i | ||||
\(119\) | −1.78357 | + | 1.29584i | −0.163500 | + | 0.118789i | ||||
\(120\) | 29.1700 | 2.66284 | ||||||||
\(121\) | −4.49516 | + | 10.0396i | −0.408650 | + | 0.912691i | ||||
\(122\) | 27.4584 | 2.48597 | ||||||||
\(123\) | −2.68140 | + | 1.94815i | −0.241774 | + | 0.175659i | ||||
\(124\) | 1.42685 | + | 4.39140i | 0.128135 | + | 0.394359i | ||||
\(125\) | 1.91029 | − | 5.87926i | 0.170861 | − | 0.525857i | ||||
\(126\) | −9.23566 | − | 6.71010i | −0.822778 | − | 0.597783i | ||||
\(127\) | −17.4005 | − | 12.6422i | −1.54404 | − | 1.12181i | −0.947734 | − | 0.319061i | \(-0.896633\pi\) |
−0.596311 | − | 0.802754i | \(-0.703367\pi\) | |||||||
\(128\) | −19.6952 | + | 60.6157i | −1.74083 | + | 5.35772i | ||||
\(129\) | 1.16027 | + | 3.57095i | 0.102156 | + | 0.314405i | ||||
\(130\) | 6.28557 | − | 4.56673i | 0.551281 | − | 0.400529i | ||||
\(131\) | 6.87944 | 0.601059 | 0.300530 | − | 0.953772i | \(-0.402837\pi\) | ||||
0.300530 | + | 0.953772i | \(0.402837\pi\) | |||||||
\(132\) | −10.3779 | − | 16.0173i | −0.903280 | − | 1.39413i | ||||
\(133\) | 1.93316 | 0.167626 | ||||||||
\(134\) | −9.33861 | + | 6.78489i | −0.806733 | + | 0.586126i | ||||
\(135\) | −0.862170 | − | 2.65349i | −0.0742038 | − | 0.228376i | ||||
\(136\) | 1.73743 | − | 5.34726i | 0.148983 | − | 0.458523i | ||||
\(137\) | −10.0232 | − | 7.28229i | −0.856341 | − | 0.622168i | 0.0705461 | − | 0.997509i | \(-0.477526\pi\) |
−0.926887 | + | 0.375340i | \(0.877526\pi\) | |||||||
\(138\) | −15.8744 | − | 11.5335i | −1.35132 | − | 0.981794i | ||||
\(139\) | −5.40773 | + | 16.6433i | −0.458678 | + | 1.41167i | 0.408084 | + | 0.912944i | \(0.366197\pi\) |
−0.866762 | + | 0.498721i | \(0.833803\pi\) | |||||||
\(140\) | 20.3392 | + | 62.5975i | 1.71897 | + | 5.29045i | ||||
\(141\) | 4.92122 | − | 3.57548i | 0.414442 | − | 0.301109i | ||||
\(142\) | 40.9082 | 3.43294 | ||||||||
\(143\) | −3.09509 | − | 1.19182i | −0.258824 | − | 0.0996647i | ||||
\(144\) | 17.6051 | 1.46709 | ||||||||
\(145\) | −6.10733 | + | 4.43724i | −0.507186 | + | 0.368492i | ||||
\(146\) | 12.1505 | + | 37.3954i | 1.00558 | + | 3.09487i | ||||
\(147\) | 3.03026 | − | 9.32619i | 0.249932 | − | 0.769211i | ||||
\(148\) | 1.49428 | + | 1.08566i | 0.122829 | + | 0.0892406i | ||||
\(149\) | 6.91960 | + | 5.02738i | 0.566875 | + | 0.411859i | 0.833969 | − | 0.551812i | \(-0.186063\pi\) |
−0.267093 | + | 0.963671i | \(0.586063\pi\) | |||||||
\(150\) | −2.39595 | + | 7.37399i | −0.195629 | + | 0.602084i | ||||
\(151\) | 3.63922 | + | 11.2004i | 0.296156 | + | 0.911473i | 0.982831 | + | 0.184509i | \(0.0590695\pi\) |
−0.686675 | + | 0.726964i | \(0.740931\pi\) | |||||||
\(152\) | −3.98856 | + | 2.89786i | −0.323515 | + | 0.235048i | ||||
\(153\) | −0.537773 | −0.0434763 | ||||||||
\(154\) | 23.8583 | − | 29.3995i | 1.92256 | − | 2.36908i | ||||
\(155\) | −2.23873 | −0.179819 | ||||||||
\(156\) | 4.65547 | − | 3.38240i | 0.372736 | − | 0.270809i | ||||
\(157\) | −2.87123 | − | 8.83673i | −0.229149 | − | 0.705248i | −0.997844 | − | 0.0656323i | \(-0.979094\pi\) |
0.768695 | − | 0.639616i | \(-0.220906\pi\) | |||||||
\(158\) | 0.922975 | − | 2.84062i | 0.0734279 | − | 0.225988i | ||||
\(159\) | 10.3763 | + | 7.53879i | 0.822891 | + | 0.597865i | ||||
\(160\) | −63.4598 | − | 46.1062i | −5.01694 | − | 3.64502i | ||||
\(161\) | 8.92650 | − | 27.4729i | 0.703506 | − | 2.16517i | ||||
\(162\) | −0.860515 | − | 2.64839i | −0.0676085 | − | 0.208078i | ||||
\(163\) | 18.4169 | − | 13.3807i | 1.44253 | − | 1.04806i | 0.455019 | − | 0.890482i | \(-0.349632\pi\) |
0.987507 | − | 0.157575i | \(-0.0503677\pi\) | |||||||
\(164\) | 19.0726 | 1.48932 | ||||||||
\(165\) | 8.94072 | − | 2.38562i | 0.696034 | − | 0.185720i | ||||
\(166\) | −4.90670 | −0.380834 | ||||||||
\(167\) | −5.71097 | + | 4.14926i | −0.441928 | + | 0.321080i | −0.786401 | − | 0.617717i | \(-0.788058\pi\) |
0.344472 | + | 0.938796i | \(0.388058\pi\) | |||||||
\(168\) | 13.2447 | + | 40.7630i | 1.02185 | + | 3.14493i | ||||
\(169\) | 0.309017 | − | 0.951057i | 0.0237705 | − | 0.0731582i | ||||
\(170\) | 3.38021 | + | 2.45586i | 0.259250 | + | 0.188356i | ||||
\(171\) | 0.381496 | + | 0.277173i | 0.0291738 | + | 0.0211960i | ||||
\(172\) | 6.67677 | − | 20.5490i | 0.509099 | − | 1.56684i | ||||
\(173\) | −2.46288 | − | 7.57996i | −0.187249 | − | 0.576293i | 0.812731 | − | 0.582639i | \(-0.197980\pi\) |
−0.999980 | + | 0.00634603i | \(0.997980\pi\) | |||||||
\(174\) | −6.09561 | + | 4.42872i | −0.462107 | + | 0.335741i | ||||
\(175\) | −11.4144 | −0.862849 | ||||||||
\(176\) | −3.11697 | + | 58.3062i | −0.234951 | + | 4.39499i | ||||
\(177\) | 0.00629823 | 0.000473404 | ||||||||
\(178\) | 13.8593 | − | 10.0694i | 1.03880 | − | 0.754731i | ||||
\(179\) | −4.22220 | − | 12.9946i | −0.315582 | − | 0.971262i | −0.975514 | − | 0.219937i | \(-0.929415\pi\) |
0.659932 | − | 0.751325i | \(-0.270585\pi\) | |||||||
\(180\) | −4.96134 | + | 15.2694i | −0.369796 | + | 1.13812i | ||||
\(181\) | −5.39818 | − | 3.92201i | −0.401244 | − | 0.291521i | 0.368804 | − | 0.929507i | \(-0.379767\pi\) |
−0.770047 | + | 0.637987i | \(0.779767\pi\) | |||||||
\(182\) | 9.23566 | + | 6.71010i | 0.684593 | + | 0.497386i | ||||
\(183\) | −3.04706 | + | 9.37790i | −0.225245 | + | 0.693234i | ||||
\(184\) | 22.7653 | + | 70.0643i | 1.67828 | + | 5.16521i | ||||
\(185\) | −0.724497 | + | 0.526378i | −0.0532661 | + | 0.0387001i | ||||
\(186\) | −2.23443 | −0.163836 | ||||||||
\(187\) | 0.0952124 | − | 1.78105i | 0.00696262 | − | 0.130243i | ||||
\(188\) | −35.0043 | −2.55295 | ||||||||
\(189\) | 3.31659 | − | 2.40964i | 0.241246 | − | 0.175276i | ||||
\(190\) | −1.13214 | − | 3.48438i | −0.0821344 | − | 0.252784i | ||||
\(191\) | 5.51100 | − | 16.9611i | 0.398762 | − | 1.22726i | −0.527231 | − | 0.849722i | \(-0.676770\pi\) |
0.925993 | − | 0.377540i | \(-0.123230\pi\) | |||||||
\(192\) | −34.8524 | − | 25.3218i | −2.51526 | − | 1.82744i | ||||
\(193\) | −11.5104 | − | 8.36276i | −0.828533 | − | 0.601965i | 0.0906108 | − | 0.995886i | \(-0.471118\pi\) |
−0.919144 | + | 0.393922i | \(0.871118\pi\) | |||||||
\(194\) | −3.11463 | + | 9.58584i | −0.223617 | + | 0.688223i | ||||
\(195\) | 0.862170 | + | 2.65349i | 0.0617413 | + | 0.190020i | ||||
\(196\) | −45.6522 | + | 33.1683i | −3.26087 | + | 2.36916i | ||||
\(197\) | 14.0364 | 1.00005 | 0.500025 | − | 0.866011i | \(-0.333324\pi\) | ||||
0.500025 | + | 0.866011i | \(0.333324\pi\) | |||||||
\(198\) | 8.92356 | − | 2.38104i | 0.634170 | − | 0.169213i | ||||
\(199\) | 4.48662 | 0.318048 | 0.159024 | − | 0.987275i | \(-0.449165\pi\) | ||||
0.159024 | + | 0.987275i | \(0.449165\pi\) | |||||||
\(200\) | 23.5507 | − | 17.1106i | 1.66528 | − | 1.20990i | ||||
\(201\) | −1.28094 | − | 3.94234i | −0.0903509 | − | 0.278071i | ||||
\(202\) | 11.2340 | − | 34.5747i | 0.790422 | − | 2.43267i | ||||
\(203\) | −8.97377 | − | 6.51983i | −0.629835 | − | 0.457602i | ||||
\(204\) | 2.50358 | + | 1.81896i | 0.175286 | + | 0.127353i | ||||
\(205\) | −2.85757 | + | 8.79471i | −0.199582 | + | 0.614249i | ||||
\(206\) | 2.38722 | + | 7.34711i | 0.166326 | + | 0.511898i | ||||
\(207\) | 5.70062 | − | 4.14175i | 0.396221 | − | 0.287871i | ||||
\(208\) | −17.6051 | −1.22069 | ||||||||
\(209\) | −0.985513 | + | 1.21440i | −0.0681694 | + | 0.0840020i | ||||
\(210\) | −31.8508 | −2.19792 | ||||||||
\(211\) | −6.81043 | + | 4.94807i | −0.468850 | + | 0.340639i | −0.796993 | − | 0.603989i | \(-0.793577\pi\) |
0.328143 | + | 0.944628i | \(0.393577\pi\) | |||||||
\(212\) | −22.8072 | − | 70.1933i | −1.56640 | − | 4.82089i | ||||
\(213\) | −4.53959 | + | 13.9714i | −0.311048 | + | 0.957306i | ||||
\(214\) | −12.8348 | − | 9.32505i | −0.877371 | − | 0.637447i | ||||
\(215\) | 8.47512 | + | 6.15754i | 0.577999 | + | 0.419941i | ||||
\(216\) | −3.23079 | + | 9.94334i | −0.219827 | + | 0.676559i | ||||
\(217\) | −1.01650 | − | 3.12846i | −0.0690044 | − | 0.212374i | ||||
\(218\) | 0.638062 | − | 0.463579i | 0.0432150 | − | 0.0313976i | ||||
\(219\) | −14.1200 | −0.954143 | ||||||||
\(220\) | −49.6924 | − | 19.1349i | −3.35026 | − | 1.29007i | ||||
\(221\) | 0.537773 | 0.0361745 | ||||||||
\(222\) | −0.723107 | + | 0.525368i | −0.0485317 | + | 0.0352604i | ||||
\(223\) | −4.78337 | − | 14.7217i | −0.320318 | − | 0.985838i | −0.973510 | − | 0.228646i | \(-0.926570\pi\) |
0.653191 | − | 0.757193i | \(-0.273430\pi\) | |||||||
\(224\) | 35.6161 | − | 109.615i | 2.37970 | − | 7.32397i | ||||
\(225\) | −2.25257 | − | 1.63658i | −0.150171 | − | 0.109106i | ||||
\(226\) | 1.25365 | + | 0.910830i | 0.0833916 | + | 0.0605875i | ||||
\(227\) | 1.64702 | − | 5.06902i | 0.109317 | − | 0.336443i | −0.881402 | − | 0.472366i | \(-0.843400\pi\) |
0.990719 | + | 0.135923i | \(0.0434001\pi\) | |||||||
\(228\) | −0.838535 | − | 2.58075i | −0.0555333 | − | 0.170914i | ||||
\(229\) | −15.0117 | + | 10.9066i | −0.992002 | + | 0.720731i | −0.960359 | − | 0.278768i | \(-0.910074\pi\) |
−0.0316432 | + | 0.999499i | \(0.510074\pi\) | |||||||
\(230\) | −54.7459 | −3.60984 | ||||||||
\(231\) | 7.39328 | + | 11.4108i | 0.486442 | + | 0.750777i | ||||
\(232\) | 28.2885 | 1.85723 | ||||||||
\(233\) | −10.6364 | + | 7.72780i | −0.696814 | + | 0.506265i | −0.878893 | − | 0.477019i | \(-0.841717\pi\) |
0.182079 | + | 0.983284i | \(0.441717\pi\) | |||||||
\(234\) | 0.860515 | + | 2.64839i | 0.0562537 | + | 0.173131i | ||||
\(235\) | 5.24455 | − | 16.1411i | 0.342117 | − | 1.05293i | ||||
\(236\) | −0.0293212 | − | 0.0213031i | −0.00190865 | − | 0.00138672i | ||||
\(237\) | 0.867738 | + | 0.630449i | 0.0563657 | + | 0.0409521i | ||||
\(238\) | −1.89710 | + | 5.83869i | −0.122971 | + | 0.378466i | ||||
\(239\) | 7.08088 | + | 21.7927i | 0.458024 | + | 1.40965i | 0.867548 | + | 0.497353i | \(0.165695\pi\) |
−0.409524 | + | 0.912299i | \(0.634305\pi\) | |||||||
\(240\) | 39.7380 | − | 28.8713i | 2.56508 | − | 1.86364i | ||||
\(241\) | 12.4123 | 0.799544 | 0.399772 | − | 0.916615i | \(-0.369089\pi\) | ||||
0.399772 | + | 0.916615i | \(0.369089\pi\) | |||||||
\(242\) | 6.30584 | + | 29.9755i | 0.405355 | + | 1.92690i | ||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 45.9053 | − | 33.3521i | 2.93879 | − | 2.13515i | ||||
\(245\) | −8.45456 | − | 26.0205i | −0.540142 | − | 1.66239i | ||||
\(246\) | −2.85209 | + | 8.77783i | −0.181843 | + | 0.559654i | ||||
\(247\) | −0.381496 | − | 0.277173i | −0.0242740 | − | 0.0176361i | ||||
\(248\) | 6.78694 | + | 4.93100i | 0.430971 | + | 0.313119i | ||||
\(249\) | 0.544497 | − | 1.67579i | 0.0345061 | − | 0.106199i | ||||
\(250\) | −5.31956 | − | 16.3719i | −0.336438 | − | 1.03545i | ||||
\(251\) | −4.67644 | + | 3.39763i | −0.295174 | + | 0.214457i | −0.725509 | − | 0.688213i | \(-0.758396\pi\) |
0.430335 | + | 0.902669i | \(0.358396\pi\) | |||||||
\(252\) | −23.5907 | −1.48607 | ||||||||
\(253\) | 12.7077 | + | 19.6132i | 0.798928 | + | 1.23307i | ||||
\(254\) | −59.8936 | −3.75806 | ||||||||
\(255\) | −1.21385 | + | 0.881917i | −0.0760145 | + | 0.0552278i | ||||
\(256\) | 28.2202 | + | 86.8529i | 1.76376 | + | 5.42830i | ||||
\(257\) | −4.94015 | + | 15.2042i | −0.308158 | + | 0.948412i | 0.670322 | + | 0.742070i | \(0.266156\pi\) |
−0.978480 | + | 0.206342i | \(0.933844\pi\) | |||||||
\(258\) | 8.45886 | + | 6.14572i | 0.526626 | + | 0.382616i | ||||
\(259\) | −1.06454 | − | 0.773430i | −0.0661470 | − | 0.0480586i | ||||
\(260\) | 4.96134 | − | 15.2694i | 0.307689 | − | 0.946970i | ||||
\(261\) | −0.836115 | − | 2.57330i | −0.0517542 | − | 0.159283i | ||||
\(262\) | 15.4984 | − | 11.2602i | 0.957494 | − | 0.695660i | ||||
\(263\) | −4.52538 | −0.279047 | −0.139524 | − | 0.990219i | \(-0.544557\pi\) | ||||
−0.139524 | + | 0.990219i | \(0.544557\pi\) | |||||||
\(264\) | −32.3593 | − | 12.4605i | −1.99158 | − | 0.766890i | ||||
\(265\) | 35.7844 | 2.19822 | ||||||||
\(266\) | 4.35513 | − | 3.16418i | 0.267030 | − | 0.194009i | ||||
\(267\) | 1.90103 | + | 5.85078i | 0.116341 | + | 0.358062i | ||||
\(268\) | −7.37117 | + | 22.6861i | −0.450266 | + | 1.38578i | ||||
\(269\) | −4.73572 | − | 3.44070i | −0.288742 | − | 0.209783i | 0.433979 | − | 0.900923i | \(-0.357109\pi\) |
−0.722721 | + | 0.691139i | \(0.757109\pi\) | |||||||
\(270\) | −6.28557 | − | 4.56673i | −0.382527 | − | 0.277922i | ||||
\(271\) | −4.33812 | + | 13.3514i | −0.263522 | + | 0.811037i | 0.728508 | + | 0.685037i | \(0.240214\pi\) |
−0.992030 | + | 0.126000i | \(0.959786\pi\) | |||||||
\(272\) | −2.92563 | − | 9.00415i | −0.177392 | − | 0.545957i | ||||
\(273\) | −3.31659 | + | 2.40964i | −0.200729 | + | 0.145838i | ||||
\(274\) | −34.5005 | −2.08425 | ||||||||
\(275\) | 5.81901 | − | 7.17051i | 0.350900 | − | 0.432398i | ||||
\(276\) | −40.5481 | −2.44071 | ||||||||
\(277\) | −4.57455 | + | 3.32361i | −0.274858 | + | 0.199696i | −0.716672 | − | 0.697411i | \(-0.754335\pi\) |
0.441813 | + | 0.897107i | \(0.354335\pi\) | |||||||
\(278\) | 15.0588 | + | 46.3464i | 0.903169 | + | 2.77967i | ||||
\(279\) | 0.247955 | − | 0.763127i | 0.0148447 | − | 0.0456872i | ||||
\(280\) | 96.7449 | + | 70.2893i | 5.78161 | + | 4.20059i | ||||
\(281\) | 16.8975 | + | 12.2767i | 1.00802 | + | 0.732369i | 0.963793 | − | 0.266652i | \(-0.0859174\pi\) |
0.0442272 | + | 0.999021i | \(0.485917\pi\) | |||||||
\(282\) | 5.23448 | − | 16.1101i | 0.311709 | − | 0.959342i | ||||
\(283\) | 6.13883 | + | 18.8934i | 0.364916 | + | 1.12309i | 0.950034 | + | 0.312147i | \(0.101048\pi\) |
−0.585118 | + | 0.810948i | \(0.698952\pi\) | |||||||
\(284\) | 68.3909 | − | 49.6889i | 4.05825 | − | 2.94849i | ||||
\(285\) | 1.31566 | 0.0779329 | ||||||||
\(286\) | −8.92356 | + | 2.38104i | −0.527661 | + | 0.140794i | ||||
\(287\) | −13.5875 | −0.802043 | ||||||||
\(288\) | 22.7451 | − | 16.5253i | 1.34027 | − | 0.973762i | ||||
\(289\) | −5.16392 | − | 15.8929i | −0.303760 | − | 0.934877i | ||||
\(290\) | −6.49610 | + | 19.9929i | −0.381464 | + | 1.17403i | ||||
\(291\) | −2.92823 | − | 2.12748i | −0.171656 | − | 0.124715i | ||||
\(292\) | 65.7354 | + | 47.7596i | 3.84687 | + | 2.79492i | ||||
\(293\) | 9.18143 | − | 28.2575i | 0.536385 | − | 1.65082i | −0.204253 | − | 0.978918i | \(-0.565477\pi\) |
0.740638 | − | 0.671904i | \(-0.234523\pi\) | |||||||
\(294\) | −8.43833 | − | 25.9705i | −0.492134 | − | 1.51463i | ||||
\(295\) | 0.0142163 | − | 0.0103288i | 0.000827706 | − | 0.000601363i | ||||
\(296\) | 3.35579 | 0.195051 | ||||||||
\(297\) | −0.177050 | + | 3.31190i | −0.0102735 | + | 0.192176i | ||||
\(298\) | 23.8177 | 1.37972 | ||||||||
\(299\) | −5.70062 | + | 4.14175i | −0.329676 | + | 0.239523i | ||||
\(300\) | 4.95117 | + | 15.2381i | 0.285856 | + | 0.879775i | ||||
\(301\) | −4.75657 | + | 14.6392i | −0.274164 | + | 0.843791i | ||||
\(302\) | 26.5314 | + | 19.2762i | 1.52671 | + | 1.10922i | ||||
\(303\) | 10.5617 | + | 7.67352i | 0.606754 | + | 0.440832i | ||||
\(304\) | −2.56539 | + | 7.89545i | −0.147135 | + | 0.452835i | ||||
\(305\) | 8.50143 | + | 26.1647i | 0.486790 | + | 1.49819i | ||||
\(306\) | −1.21153 | + | 0.880225i | −0.0692583 | + | 0.0503191i | ||||
\(307\) | −9.70302 | −0.553781 | −0.276890 | − | 0.960902i | \(-0.589304\pi\) | ||||
−0.276890 | + | 0.960902i | \(0.589304\pi\) | |||||||
\(308\) | 4.17672 | − | 78.1298i | 0.237990 | − | 4.45186i | ||||
\(309\) | −2.77418 | −0.157817 | ||||||||
\(310\) | −5.04353 | + | 3.66434i | −0.286453 | + | 0.208121i | ||||
\(311\) | 0.774571 | + | 2.38389i | 0.0439219 | + | 0.135178i | 0.970613 | − | 0.240647i | \(-0.0773595\pi\) |
−0.926691 | + | 0.375825i | \(0.877360\pi\) | |||||||
\(312\) | 3.23079 | − | 9.94334i | 0.182907 | − | 0.562931i | ||||
\(313\) | −24.9880 | − | 18.1548i | −1.41240 | − | 1.02617i | −0.992968 | − | 0.118386i | \(-0.962228\pi\) |
−0.419436 | − | 0.907785i | \(-0.637772\pi\) | |||||||
\(314\) | −20.9324 | − | 15.2083i | −1.18128 | − | 0.858253i | ||||
\(315\) | 3.53449 | − | 10.8780i | 0.199146 | − | 0.612908i | ||||
\(316\) | −1.90730 | − | 5.87007i | −0.107294 | − | 0.330217i | ||||
\(317\) | −2.33944 | + | 1.69970i | −0.131396 | + | 0.0954648i | −0.651542 | − | 0.758613i | \(-0.725878\pi\) |
0.520146 | + | 0.854077i | \(0.325878\pi\) | |||||||
\(318\) | 35.7157 | 2.00284 | ||||||||
\(319\) | 8.67052 | − | 2.31352i | 0.485456 | − | 0.129532i | ||||
\(320\) | −120.195 | −6.71909 | ||||||||
\(321\) | 4.60908 | − | 3.34869i | 0.257254 | − | 0.186906i | ||||
\(322\) | −24.8575 | − | 76.5035i | −1.38525 | − | 4.26337i | ||||
\(323\) | 0.0783635 | − | 0.241178i | 0.00436026 | − | 0.0134195i | ||||
\(324\) | −4.65547 | − | 3.38240i | −0.258637 | − | 0.187911i | ||||
\(325\) | 2.25257 | + | 1.63658i | 0.124950 | + | 0.0907814i | ||||
\(326\) | 19.5893 | − | 60.2896i | 1.08495 | − | 3.33913i | ||||
\(327\) | 0.0875209 | + | 0.269361i | 0.00483991 | + | 0.0148957i | ||||
\(328\) | 28.0342 | − | 20.3680i | 1.54793 | − | 1.12464i | ||||
\(329\) | 24.9373 | 1.37484 | ||||||||
\(330\) | 16.2374 | − | 20.0086i | 0.893839 | − | 1.10144i | ||||
\(331\) | −13.4774 | −0.740785 | −0.370392 | − | 0.928875i | \(-0.620777\pi\) | ||||
−0.370392 | + | 0.928875i | \(0.620777\pi\) | |||||||
\(332\) | −8.20308 | + | 5.95989i | −0.450203 | + | 0.327091i | ||||
\(333\) | −0.0991861 | − | 0.305263i | −0.00543536 | − | 0.0167283i | ||||
\(334\) | −6.07451 | + | 18.6954i | −0.332382 | + | 1.02297i | ||||
\(335\) | −9.35656 | − | 6.79794i | −0.511203 | − | 0.371411i | ||||
\(336\) | 58.3888 | + | 42.4219i | 3.18537 | + | 2.31431i | ||||
\(337\) | −6.66618 | + | 20.5164i | −0.363130 | + | 1.11760i | 0.588014 | + | 0.808851i | \(0.299910\pi\) |
−0.951144 | + | 0.308749i | \(0.900090\pi\) | |||||||
\(338\) | −0.860515 | − | 2.64839i | −0.0468059 | − | 0.144054i | ||||
\(339\) | −0.450194 | + | 0.327085i | −0.0244512 | + | 0.0177648i | ||||
\(340\) | 8.63406 | 0.468248 | ||||||||
\(341\) | 2.48350 | + | 0.956312i | 0.134489 | + | 0.0517872i | ||||
\(342\) | 1.31313 | 0.0710062 | ||||||||
\(343\) | 9.30681 | − | 6.76179i | 0.502520 | − | 0.365102i | ||||
\(344\) | −12.1307 | − | 37.3345i | −0.654044 | − | 2.01294i | ||||
\(345\) | 6.07516 | − | 18.6974i | 0.327075 | − | 1.00663i | ||||
\(346\) | −17.9554 | − | 13.0453i | −0.965286 | − | 0.701322i | ||||
\(347\) | −22.4397 | − | 16.3034i | −1.20463 | − | 0.875214i | −0.209896 | − | 0.977724i | \(-0.567313\pi\) |
−0.994732 | + | 0.102510i | \(0.967313\pi\) | |||||||
\(348\) | −4.81140 | + | 14.8080i | −0.257918 | + | 0.793791i | ||||
\(349\) | 3.59928 | + | 11.0774i | 0.192665 | + | 0.592961i | 0.999996 | + | 0.00286254i | \(0.000911177\pi\) |
−0.807331 | + | 0.590099i | \(0.799089\pi\) | |||||||
\(350\) | −25.7151 | + | 18.6831i | −1.37453 | + | 0.998653i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 50.7030 | + | 78.2553i | 2.70248 | + | 4.17102i | ||||
\(353\) | 23.2708 | 1.23858 | 0.619291 | − | 0.785161i | \(-0.287420\pi\) | ||||
0.619291 | + | 0.785161i | \(0.287420\pi\) | |||||||
\(354\) | 0.0141890 | − | 0.0103089i | 0.000754138 | − | 0.000547914i | ||||
\(355\) | 12.6656 | + | 38.9808i | 0.672223 | + | 2.06889i | ||||
\(356\) | 10.9395 | − | 33.6682i | 0.579790 | − | 1.78441i | ||||
\(357\) | −1.78357 | − | 1.29584i | −0.0943966 | − | 0.0685831i | ||||
\(358\) | −30.7816 | − | 22.3641i | −1.62686 | − | 1.18198i | ||||
\(359\) | −9.21852 | + | 28.3717i | −0.486535 | + | 1.49740i | 0.343211 | + | 0.939258i | \(0.388485\pi\) |
−0.829746 | + | 0.558142i | \(0.811515\pi\) | |||||||
\(360\) | 9.01403 | + | 27.7423i | 0.475081 | + | 1.46215i | ||||
\(361\) | 15.1914 | − | 11.0372i | 0.799549 | − | 0.580906i | ||||
\(362\) | −18.5809 | −0.976589 | ||||||||
\(363\) | −10.9373 | − | 1.17274i | −0.574060 | − | 0.0615529i | ||||
\(364\) | 23.5907 | 1.23649 | ||||||||
\(365\) | −31.8716 | + | 23.1561i | −1.66824 | + | 1.21204i | ||||
\(366\) | 8.48512 | + | 26.1145i | 0.443524 | + | 1.36503i | ||||
\(367\) | −2.85508 | + | 8.78702i | −0.149034 | + | 0.458679i | −0.997508 | − | 0.0705585i | \(-0.977522\pi\) |
0.848474 | + | 0.529237i | \(0.177522\pi\) | |||||||
\(368\) | 100.360 | + | 72.9157i | 5.23162 | + | 3.80099i | ||||
\(369\) | −2.68140 | − | 1.94815i | −0.139588 | − | 0.101417i | ||||
\(370\) | −0.770615 | + | 2.37171i | −0.0400624 | + | 0.123299i | ||||
\(371\) | 16.2480 | + | 50.0061i | 0.843553 | + | 2.59619i | ||||
\(372\) | −3.73555 | + | 2.71403i | −0.193679 | + | 0.140716i | ||||
\(373\) | 9.45574 | 0.489600 | 0.244800 | − | 0.969574i | \(-0.421278\pi\) | ||||
0.244800 | + | 0.969574i | \(0.421278\pi\) | |||||||
\(374\) | −2.70071 | − | 4.16829i | −0.139651 | − | 0.215537i | ||||
\(375\) | 6.18182 | 0.319228 | ||||||||
\(376\) | −51.4516 | + | 37.3818i | −2.65341 | + | 1.92782i | ||||
\(377\) | 0.836115 | + | 2.57330i | 0.0430621 | + | 0.132532i | ||||
\(378\) | 3.52771 | − | 10.8572i | 0.181446 | − | 0.558433i | ||||
\(379\) | −9.22696 | − | 6.70378i | −0.473957 | − | 0.344350i | 0.325024 | − | 0.945706i | \(-0.394627\pi\) |
−0.798981 | + | 0.601356i | \(0.794627\pi\) | |||||||
\(380\) | −6.12501 | − | 4.45008i | −0.314207 | − | 0.228284i | ||||
\(381\) | 6.64640 | − | 20.4555i | 0.340505 | − | 1.04797i | ||||
\(382\) | −15.3464 | − | 47.2313i | −0.785190 | − | 2.41657i | ||||
\(383\) | 28.9202 | − | 21.0117i | 1.47775 | − | 1.07365i | 0.499480 | − | 0.866325i | \(-0.333524\pi\) |
0.978272 | − | 0.207325i | \(-0.0664756\pi\) | |||||||
\(384\) | −63.7352 | −3.25247 | ||||||||
\(385\) | 35.4012 | + | 13.6318i | 1.80421 | + | 0.694742i | ||||
\(386\) | −39.6193 | −2.01657 | ||||||||
\(387\) | −3.03763 | + | 2.20697i | −0.154412 | + | 0.112187i | ||||
\(388\) | 6.43630 | + | 19.8089i | 0.326753 | + | 1.00564i | ||||
\(389\) | −3.39313 | + | 10.4430i | −0.172038 | + | 0.529480i | −0.999486 | − | 0.0320634i | \(-0.989792\pi\) |
0.827447 | + | 0.561543i | \(0.189792\pi\) | |||||||
\(390\) | 6.28557 | + | 4.56673i | 0.318282 | + | 0.231245i | ||||
\(391\) | −3.06564 | − | 2.22732i | −0.155036 | − | 0.112640i | ||||
\(392\) | −31.6815 | + | 97.5058i | −1.60016 | + | 4.92479i | ||||
\(393\) | 2.12586 | + | 6.54273i | 0.107236 | + | 0.330037i | ||||
\(394\) | 31.6220 | − | 22.9747i | 1.59309 | − | 1.15745i | ||||
\(395\) | 2.99255 | 0.150572 | ||||||||
\(396\) | 12.0264 | − | 14.8196i | 0.604349 | − | 0.744712i | ||||
\(397\) | −8.71624 | −0.437456 | −0.218728 | − | 0.975786i | \(-0.570191\pi\) | ||||
−0.218728 | + | 0.975786i | \(0.570191\pi\) | |||||||
\(398\) | 10.1077 | − | 7.34369i | 0.506655 | − | 0.368106i | ||||
\(399\) | 0.597378 | + | 1.83854i | 0.0299063 | + | 0.0920421i | ||||
\(400\) | 15.1475 | − | 46.6191i | 0.757373 | − | 2.33096i | ||||
\(401\) | −26.9918 | − | 19.6107i | −1.34791 | − | 0.979311i | −0.999113 | − | 0.0421114i | \(-0.986592\pi\) |
−0.348793 | − | 0.937200i | \(-0.613408\pi\) | |||||||
\(402\) | −9.33861 | − | 6.78489i | −0.465767 | − | 0.338400i | ||||
\(403\) | −0.247955 | + | 0.763127i | −0.0123515 | + | 0.0380141i | ||||
\(404\) | −23.2148 | − | 71.4477i | −1.15498 | − | 3.55466i | ||||
\(405\) | 2.25719 | − | 1.63994i | 0.112161 | − | 0.0814895i | ||||
\(406\) | −30.8883 | −1.53296 | ||||||||
\(407\) | 1.02856 | − | 0.274447i | 0.0509839 | − | 0.0136038i | ||||
\(408\) | 5.62244 | 0.278352 | ||||||||
\(409\) | 27.1252 | − | 19.7076i | 1.34126 | − | 0.974480i | 0.341860 | − | 0.939751i | \(-0.388943\pi\) |
0.999397 | − | 0.0347288i | \(-0.0110568\pi\) | |||||||
\(410\) | 7.95744 | + | 24.4905i | 0.392990 | + | 1.20950i | ||||
\(411\) | 3.82853 | − | 11.7830i | 0.188847 | − | 0.581212i | ||||
\(412\) | 12.9151 | + | 9.38337i | 0.636281 | + | 0.462285i | ||||
\(413\) | 0.0208887 | + | 0.0151765i | 0.00102786 | + | 0.000746786i | ||||
\(414\) | 6.06350 | − | 18.6615i | 0.298005 | − | 0.917164i | ||||
\(415\) | −1.51917 | − | 4.67552i | −0.0745731 | − | 0.229512i | ||||
\(416\) | −22.7451 | + | 16.5253i | −1.11517 | + | 0.810219i | ||||
\(417\) | −17.4998 | −0.856969 | ||||||||
\(418\) | −0.232490 | + | 4.34896i | −0.0113715 | + | 0.212715i | ||||
\(419\) | 8.26093 | 0.403573 | 0.201786 | − | 0.979430i | \(-0.435325\pi\) | ||||
0.201786 | + | 0.979430i | \(0.435325\pi\) | |||||||
\(420\) | −53.2486 | + | 38.6874i | −2.59827 | + | 1.88775i | ||||
\(421\) | −2.20317 | − | 6.78065i | −0.107376 | − | 0.330469i | 0.882905 | − | 0.469552i | \(-0.155585\pi\) |
−0.990281 | + | 0.139083i | \(0.955585\pi\) | |||||||
\(422\) | −7.24396 | + | 22.2946i | −0.352630 | + | 1.08528i | ||||
\(423\) | 4.92122 | + | 3.57548i | 0.239278 | + | 0.173846i | ||||
\(424\) | −108.484 | − | 78.8184i | −5.26846 | − | 3.82776i | ||||
\(425\) | −0.462701 | + | 1.42405i | −0.0224443 | + | 0.0690765i | ||||
\(426\) | 12.6413 | + | 38.9060i | 0.612475 | + | 1.88500i | ||||
\(427\) | −32.7032 | + | 23.7603i | −1.58262 | + | 1.14984i | ||||
\(428\) | −32.7840 | −1.58468 | ||||||||
\(429\) | 0.177050 | − | 3.31190i | 0.00854804 | − | 0.159900i | ||||
\(430\) | 29.1719 | 1.40679 | ||||||||
\(431\) | 20.2346 | − | 14.7013i | 0.974666 | − | 0.708136i | 0.0181557 | − | 0.999835i | \(-0.494221\pi\) |
0.956510 | + | 0.291699i | \(0.0942205\pi\) | |||||||
\(432\) | 5.44027 | + | 16.7434i | 0.261745 | + | 0.805568i | ||||
\(433\) | −4.05466 | + | 12.4790i | −0.194855 | + | 0.599701i | 0.805124 | + | 0.593107i | \(0.202099\pi\) |
−0.999978 | + | 0.00659404i | \(0.997901\pi\) | |||||||
\(434\) | −7.41069 | − | 5.38418i | −0.355724 | − | 0.258449i | ||||
\(435\) | −6.10733 | − | 4.43724i | −0.292824 | − | 0.212749i | ||||
\(436\) | 0.503637 | − | 1.55004i | 0.0241198 | − | 0.0742332i | ||||
\(437\) | 1.02679 | + | 3.16012i | 0.0491178 | + | 0.151169i | ||||
\(438\) | −31.8104 | + | 23.1116i | −1.51996 | + | 1.10432i | ||||
\(439\) | −23.2672 | −1.11048 | −0.555242 | − | 0.831689i | \(-0.687374\pi\) | ||||
−0.555242 | + | 0.831689i | \(0.687374\pi\) | |||||||
\(440\) | −93.4756 | + | 24.9417i | −4.45627 | + | 1.18905i | ||||
\(441\) | 9.80614 | 0.466959 | ||||||||
\(442\) | 1.21153 | − | 0.880225i | 0.0576264 | − | 0.0418680i | ||||
\(443\) | 10.1396 | + | 31.2065i | 0.481748 | + | 1.48267i | 0.836637 | + | 0.547758i | \(0.184519\pi\) |
−0.354889 | + | 0.934908i | \(0.615481\pi\) | |||||||
\(444\) | −0.570764 | + | 1.75663i | −0.0270873 | + | 0.0833661i | ||||
\(445\) | 13.8859 | + | 10.0887i | 0.658257 | + | 0.478252i | ||||
\(446\) | −34.8727 | − | 25.3365i | −1.65127 | − | 1.19972i | ||||
\(447\) | −2.64305 | + | 8.13447i | −0.125012 | + | 0.384747i | ||||
\(448\) | −54.5747 | − | 167.964i | −2.57841 | − | 7.93554i | ||||
\(449\) | −14.4756 | + | 10.5172i | −0.683148 | + | 0.496336i | −0.874401 | − | 0.485205i | \(-0.838745\pi\) |
0.191253 | + | 0.981541i | \(0.438745\pi\) | |||||||
\(450\) | −7.75347 | −0.365502 | ||||||||
\(451\) | 6.92682 | − | 8.53561i | 0.326171 | − | 0.401926i | ||||
\(452\) | 3.20220 | 0.150619 | ||||||||
\(453\) | −9.52761 | + | 6.92221i | −0.447646 | + | 0.325234i | ||||
\(454\) | −4.58645 | − | 14.1156i | −0.215253 | − | 0.662480i | ||||
\(455\) | −3.53449 | + | 10.8780i | −0.165699 | + | 0.509971i | ||||
\(456\) | −3.98856 | − | 2.89786i | −0.186782 | − | 0.135705i | ||||
\(457\) | 17.6397 | + | 12.8160i | 0.825152 | + | 0.599508i | 0.918184 | − | 0.396155i | \(-0.129656\pi\) |
−0.0930317 | + | 0.995663i | \(0.529656\pi\) | |||||||
\(458\) | −15.9673 | + | 49.1423i | −0.746102 | + | 2.29627i | ||||
\(459\) | −0.166181 | − | 0.511452i | −0.00775666 | − | 0.0238725i | ||||
\(460\) | −91.5248 | + | 66.4967i | −4.26737 | + | 3.10042i | ||||
\(461\) | 15.4094 | 0.717688 | 0.358844 | − | 0.933398i | \(-0.383171\pi\) | ||||
0.358844 | + | 0.933398i | \(0.383171\pi\) | |||||||
\(462\) | 35.3332 | + | 13.6057i | 1.64385 | + | 0.632993i | ||||
\(463\) | 31.2592 | 1.45274 | 0.726369 | − | 0.687305i | \(-0.241206\pi\) | ||||
0.726369 | + | 0.687305i | \(0.241206\pi\) | |||||||
\(464\) | 38.5371 | − | 27.9988i | 1.78904 | − | 1.29981i | ||||
\(465\) | −0.691804 | − | 2.12916i | −0.0320817 | − | 0.0987372i | ||||
\(466\) | −11.3135 | + | 34.8193i | −0.524087 | + | 1.61297i | ||||
\(467\) | 10.6569 | + | 7.74267i | 0.493141 | + | 0.358288i | 0.806391 | − | 0.591383i | \(-0.201418\pi\) |
−0.313250 | + | 0.949671i | \(0.601418\pi\) | |||||||
\(468\) | 4.65547 | + | 3.38240i | 0.215199 | + | 0.156351i | ||||
\(469\) | 5.25127 | − | 16.1618i | 0.242481 | − | 0.746280i | ||||
\(470\) | −14.6044 | − | 44.9478i | −0.673652 | − | 2.07329i | ||||
\(471\) | 7.51697 | − | 5.46140i | 0.346364 | − | 0.251648i | ||||
\(472\) | −0.0658483 | −0.00303092 | ||||||||
\(473\) | −6.77145 | − | 10.4511i | −0.311351 | − | 0.480541i | ||||
\(474\) | 2.98681 | 0.137189 | ||||||||
\(475\) | 1.06221 | − | 0.771741i | 0.0487375 | − | 0.0354099i | ||||
\(476\) | 3.92032 | + | 12.0655i | 0.179687 | + | 0.553021i | ||||
\(477\) | −3.96338 | + | 12.1980i | −0.181471 | + | 0.558509i | ||||
\(478\) | 51.6224 | + | 37.5059i | 2.36116 | + | 1.71548i | ||||
\(479\) | −10.1560 | − | 7.37876i | −0.464039 | − | 0.337144i | 0.331075 | − | 0.943605i | \(-0.392589\pi\) |
−0.795114 | + | 0.606461i | \(0.792589\pi\) | |||||||
\(480\) | 24.2395 | − | 74.6015i | 1.10638 | − | 3.40508i | ||||
\(481\) | 0.0991861 | + | 0.305263i | 0.00452250 | + | 0.0139188i | ||||
\(482\) | 27.9631 | − | 20.3164i | 1.27368 | − | 0.925385i | ||||
\(483\) | 28.8868 | 1.31439 | ||||||||
\(484\) | 46.9516 | + | 42.4540i | 2.13417 | + | 1.92973i | ||||
\(485\) | −10.0985 | −0.458551 | ||||||||
\(486\) | 2.25286 | − | 1.63680i | 0.102192 | − | 0.0742467i | ||||
\(487\) | 2.44119 | + | 7.51320i | 0.110621 | + | 0.340455i | 0.991008 | − | 0.133799i | \(-0.0427177\pi\) |
−0.880388 | + | 0.474254i | \(0.842718\pi\) | |||||||
\(488\) | 31.8572 | − | 98.0463i | 1.44211 | − | 4.43835i | ||||
\(489\) | 18.4169 | + | 13.3807i | 0.832843 | + | 0.605096i | ||||
\(490\) | −61.6371 | − | 44.7820i | −2.78448 | − | 2.02304i | ||||
\(491\) | −0.633004 | + | 1.94818i | −0.0285671 | + | 0.0879203i | −0.964324 | − | 0.264727i | \(-0.914718\pi\) |
0.935756 | + | 0.352647i | \(0.114718\pi\) | |||||||
\(492\) | 5.89377 | + | 18.1391i | 0.265711 | + | 0.817776i | ||||
\(493\) | −1.17717 | + | 0.855265i | −0.0530171 | + | 0.0385192i | ||||
\(494\) | −1.31313 | −0.0590807 | ||||||||
\(495\) | 5.03169 | + | 7.76593i | 0.226158 | + | 0.349053i | ||||
\(496\) | 14.1263 | 0.634289 | ||||||||
\(497\) | −48.7221 | + | 35.3987i | −2.18549 | + | 1.58785i | ||||
\(498\) | −1.51625 | − | 4.66655i | −0.0679450 | − | 0.209113i | ||||
\(499\) | −7.95426 | + | 24.4807i | −0.356082 | + | 1.09591i | 0.599298 | + | 0.800526i | \(0.295447\pi\) |
−0.955380 | + | 0.295381i | \(0.904553\pi\) | |||||||
\(500\) | −28.7793 | − | 20.9094i | −1.28705 | − | 0.935096i | ||||
\(501\) | −5.71097 | − | 4.14926i | −0.255147 | − | 0.185375i | ||||
\(502\) | −4.97412 | + | 15.3088i | −0.222006 | + | 0.683264i | ||||
\(503\) | −6.59639 | − | 20.3016i | −0.294119 | − | 0.905204i | −0.983516 | − | 0.180821i | \(-0.942125\pi\) |
0.689398 | − | 0.724383i | \(-0.257875\pi\) | |||||||
\(504\) | −34.6751 | + | 25.1929i | −1.54455 | + | 1.12218i | ||||
\(505\) | 36.4239 | 1.62084 | ||||||||
\(506\) | 60.7315 | + | 23.3857i | 2.69985 | + | 1.03962i | ||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | −100.131 | + | 72.7493i | −4.44259 | + | 3.22773i | ||||
\(509\) | 5.20633 | + | 16.0234i | 0.230766 | + | 0.710226i | 0.997655 | + | 0.0684456i | \(0.0218040\pi\) |
−0.766888 | + | 0.641780i | \(0.778196\pi\) | |||||||
\(510\) | −1.29112 | + | 3.97367i | −0.0571719 | + | 0.175957i | ||||
\(511\) | −46.8303 | − | 34.0242i | −2.07165 | − | 1.50514i | ||||
\(512\) | 102.611 | + | 74.5513i | 4.53481 | + | 3.29473i | ||||
\(513\) | −0.145719 | + | 0.448476i | −0.00643364 | + | 0.0198007i | ||||
\(514\) | 13.7568 | + | 42.3389i | 0.606785 | + | 1.86749i | ||||
\(515\) | −6.26184 | + | 4.54949i | −0.275930 | + | 0.200475i | ||||
\(516\) | 21.6065 | 0.951172 | ||||||||
\(517\) | −12.7129 | + | 15.6655i | −0.559113 | + | 0.688969i | ||||
\(518\) | −3.66420 | −0.160996 | ||||||||
\(519\) | 6.44790 | − | 4.68467i | 0.283031 | − | 0.205634i | ||||
\(520\) | −9.01403 | − | 27.7423i | −0.395291 | − | 1.21658i | ||||
\(521\) | −0.429309 | + | 1.32128i | −0.0188084 | + | 0.0578863i | −0.960020 | − | 0.279931i | \(-0.909688\pi\) |
0.941212 | + | 0.337817i | \(0.109688\pi\) | |||||||
\(522\) | −6.09561 | − | 4.42872i | −0.266798 | − | 0.193840i | ||||
\(523\) | 0.718852 | + | 0.522276i | 0.0314332 | + | 0.0228376i | 0.603391 | − | 0.797446i | \(-0.293816\pi\) |
−0.571958 | + | 0.820283i | \(0.693816\pi\) | |||||||
\(524\) | 12.2332 | − | 37.6500i | 0.534411 | − | 1.64475i | ||||
\(525\) | −3.52725 | − | 10.8558i | −0.153942 | − | 0.473784i | ||||
\(526\) | −10.1950 | + | 7.40713i | −0.444525 | + | 0.322966i | ||||
\(527\) | −0.431508 | −0.0187968 | ||||||||
\(528\) | −56.4157 | + | 15.0532i | −2.45518 | + | 0.655106i | ||||
\(529\) | 26.6512 | 1.15875 | ||||||||
\(530\) | 80.6172 | − | 58.5718i | 3.50179 | − | 2.54420i | ||||
\(531\) | 0.00194626 | + | 0.00598998i | 8.44605e−5 | + | 0.000259943i | ||||
\(532\) | 3.43760 | − | 10.5798i | 0.149039 | − | 0.458694i | ||||
\(533\) | 2.68140 | + | 1.94815i | 0.116144 | + | 0.0843839i | ||||
\(534\) | 13.8593 | + | 10.0694i | 0.599750 | + | 0.435744i | ||||
\(535\) | 4.91190 | − | 15.1173i | 0.212360 | − | 0.653576i | ||||
\(536\) | 13.3923 | + | 41.2174i | 0.578461 | + | 1.78032i | ||||
\(537\) | 11.0539 | − | 8.03110i | 0.477010 | − | 0.346568i | ||||
\(538\) | −16.3006 | −0.702771 | ||||||||
\(539\) | −1.73617 | + | 32.4769i | −0.0747823 | + | 1.39888i | ||||
\(540\) | −16.0552 | −0.690907 | ||||||||
\(541\) | 11.3076 | − | 8.21548i | 0.486154 | − | 0.353211i | −0.317550 | − | 0.948242i | \(-0.602860\pi\) |
0.803703 | + | 0.595030i | \(0.202860\pi\) | |||||||
\(542\) | 12.0803 | + | 37.1793i | 0.518893 | + | 1.59699i | ||||
\(543\) | 2.06192 | − | 6.34594i | 0.0884855 | − | 0.272330i | ||||
\(544\) | −12.2317 | − | 8.88685i | −0.524430 | − | 0.381021i | ||||
\(545\) | 0.639289 | + | 0.464471i | 0.0273841 | + | 0.0198957i | ||||
\(546\) | −3.52771 | + | 10.8572i | −0.150972 | + | 0.464644i | ||||
\(547\) | 0.0977966 | + | 0.300987i | 0.00418148 | + | 0.0128693i | 0.953125 | − | 0.302575i | \(-0.0978464\pi\) |
−0.948944 | + | 0.315445i | \(0.897846\pi\) | |||||||
\(548\) | −57.6784 | + | 41.9058i | −2.46390 | + | 1.79013i | ||||
\(549\) | −9.86050 | −0.420836 | ||||||||
\(550\) | 1.37275 | − | 25.6787i | 0.0585342 | − | 1.09494i | ||||
\(551\) | 1.27590 | 0.0543551 | ||||||||
\(552\) | −59.6003 | + | 43.3021i | −2.53676 | + | 1.84306i | ||||
\(553\) | 1.35877 | + | 4.18188i | 0.0577810 | + | 0.177832i | ||||
\(554\) | −4.86575 | + | 14.9752i | −0.206726 | + | 0.636236i | ||||
\(555\) | −0.724497 | − | 0.526378i | −0.0307532 | − | 0.0223435i | ||||
\(556\) | 81.4698 | + | 59.1913i | 3.45509 | + | 2.51027i | ||||
\(557\) | 11.0442 | − | 33.9904i | 0.467956 | − | 1.44022i | −0.387270 | − | 0.921966i | \(-0.626582\pi\) |
0.855226 | − | 0.518255i | \(-0.173418\pi\) | |||||||
\(558\) | −0.690477 | − | 2.12507i | −0.0292302 | − | 0.0899614i | ||||
\(559\) | 3.03763 | − | 2.20697i | 0.128478 | − | 0.0933449i | ||||
\(560\) | 201.364 | 8.50919 | ||||||||
\(561\) | 1.72330 | − | 0.459821i | 0.0727577 | − | 0.0194137i | ||||
\(562\) | 58.1622 | 2.45343 | ||||||||
\(563\) | −30.1356 | + | 21.8948i | −1.27006 | + | 0.922755i | −0.999205 | − | 0.0398643i | \(-0.987307\pi\) |
−0.270858 | + | 0.962619i | \(0.587307\pi\) | |||||||
\(564\) | −10.8169 | − | 33.2911i | −0.455474 | − | 1.40181i | ||||
\(565\) | −0.479772 | + | 1.47659i | −0.0201842 | + | 0.0621205i | ||||
\(566\) | 44.7546 | + | 32.5161i | 1.88117 | + | 1.36675i | ||||
\(567\) | 3.31659 | + | 2.40964i | 0.139284 | + | 0.101195i | ||||
\(568\) | 47.4616 | − | 146.072i | 1.99145 | − | 6.12904i | ||||
\(569\) | −2.44848 | − | 7.53565i | −0.102646 | − | 0.315911i | 0.886525 | − | 0.462681i | \(-0.153112\pi\) |
−0.989171 | + | 0.146770i | \(0.953112\pi\) | |||||||
\(570\) | 2.96399 | − | 2.15347i | 0.124148 | − | 0.0901988i | ||||
\(571\) | 4.43525 | 0.185609 | 0.0928047 | − | 0.995684i | \(-0.470417\pi\) | ||||
0.0928047 | + | 0.995684i | \(0.470417\pi\) | |||||||
\(572\) | −12.0264 | + | 14.8196i | −0.502849 | + | 0.619638i | ||||
\(573\) | 17.8340 | 0.745024 | ||||||||
\(574\) | −30.6106 | + | 22.2399i | −1.27766 | + | 0.928277i | ||||
\(575\) | −6.06271 | − | 18.6591i | −0.252833 | − | 0.778139i | ||||
\(576\) | 13.3124 | − | 40.9715i | 0.554685 | − | 1.70714i | ||||
\(577\) | 8.96744 | + | 6.51522i | 0.373319 | + | 0.271232i | 0.758586 | − | 0.651573i | \(-0.225891\pi\) |
−0.385267 | + | 0.922805i | \(0.625891\pi\) | |||||||
\(578\) | −37.6471 | − | 27.3522i | −1.56591 | − | 1.13770i | ||||
\(579\) | 4.39656 | − | 13.5312i | 0.182715 | − | 0.562339i | ||||
\(580\) | 13.4240 | + | 41.3149i | 0.557402 | + | 1.71551i | ||||
\(581\) | 5.84393 | − | 4.24586i | 0.242447 | − | 0.176148i | ||||
\(582\) | −10.0792 | −0.417794 | ||||||||
\(583\) | −39.6969 | − | 15.2859i | −1.64408 | − | 0.633079i | ||||
\(584\) | 147.626 | 6.10879 | ||||||||
\(585\) | −2.25719 | + | 1.63994i | −0.0933233 | + | 0.0678034i | ||||
\(586\) | −25.5674 | − | 78.6884i | −1.05618 | − | 3.25059i | ||||
\(587\) | −6.14070 | + | 18.8991i | −0.253454 | + | 0.780051i | 0.740676 | + | 0.671862i | \(0.234505\pi\) |
−0.994130 | + | 0.108189i | \(0.965495\pi\) | |||||||
\(588\) | −45.6522 | − | 33.1683i | −1.88266 | − | 1.36784i | ||||
\(589\) | 0.306112 | + | 0.222404i | 0.0126131 | + | 0.00916399i | ||||
\(590\) | 0.0151213 | − | 0.0465384i | 0.000622532 | − | 0.00191596i | ||||
\(591\) | 4.33748 | + | 13.3494i | 0.178420 | + | 0.549120i | ||||
\(592\) | 4.57155 | − | 3.32143i | 0.187890 | − | 0.136510i | ||||
\(593\) | 23.1858 | 0.952127 | 0.476064 | − | 0.879411i | \(-0.342063\pi\) | ||||
0.476064 | + | 0.879411i | \(0.342063\pi\) | |||||||
\(594\) | 5.02204 | + | 7.75103i | 0.206057 | + | 0.318029i | ||||
\(595\) | −6.15096 | −0.252165 | ||||||||
\(596\) | 39.8187 | − | 28.9300i | 1.63104 | − | 1.18502i | ||||
\(597\) | 1.38644 | + | 4.26703i | 0.0567433 | + | 0.174638i | ||||
\(598\) | −6.06350 | + | 18.6615i | −0.247955 | + | 0.763127i | ||||
\(599\) | −16.4590 | − | 11.9582i | −0.672498 | − | 0.488598i | 0.198362 | − | 0.980129i | \(-0.436438\pi\) |
−0.870860 | + | 0.491530i | \(0.836438\pi\) | |||||||
\(600\) | 23.5507 | + | 17.1106i | 0.961453 | + | 0.698536i | ||||
\(601\) | 7.28686 | − | 22.4267i | 0.297237 | − | 0.914802i | −0.685224 | − | 0.728333i | \(-0.740295\pi\) |
0.982461 | − | 0.186469i | \(-0.0597045\pi\) | |||||||
\(602\) | 13.2456 | + | 40.7657i | 0.539849 | + | 1.66148i | ||||
\(603\) | 3.35356 | − | 2.43650i | 0.136567 | − | 0.0992220i | ||||
\(604\) | 67.7692 | 2.75749 | ||||||||
\(605\) | −26.6108 | + | 15.2895i | −1.08188 | + | 0.621606i | ||||
\(606\) | 36.3540 | 1.47678 | ||||||||
\(607\) | −3.36147 | + | 2.44225i | −0.136438 | + | 0.0991278i | −0.653911 | − | 0.756572i | \(-0.726873\pi\) |
0.517473 | + | 0.855700i | \(0.326873\pi\) | |||||||
\(608\) | 4.09681 | + | 12.6087i | 0.166148 | + | 0.511350i | ||||
\(609\) | 3.42768 | − | 10.5493i | 0.138896 | − | 0.427479i | ||||
\(610\) | 61.9788 | + | 45.0303i | 2.50945 | + | 1.82322i | ||||
\(611\) | −4.92122 | − | 3.57548i | −0.199091 | − | 0.144648i | ||||
\(612\) | −0.956284 | + | 2.94314i | −0.0386555 | + | 0.118969i | ||||
\(613\) | 3.02768 | + | 9.31824i | 0.122287 | + | 0.376360i | 0.993397 | − | 0.114728i | \(-0.0365995\pi\) |
−0.871110 | + | 0.491088i | \(0.836599\pi\) | |||||||
\(614\) | −21.8595 | + | 15.8819i | −0.882179 | + | 0.640941i | ||||
\(615\) | −9.24730 | −0.372887 | ||||||||
\(616\) | −77.2971 | − | 119.301i | −3.11439 | − | 4.80676i | ||||
\(617\) | −11.1642 | −0.449454 | −0.224727 | − | 0.974422i | \(-0.572149\pi\) | ||||
−0.224727 | + | 0.974422i | \(0.572149\pi\) | |||||||
\(618\) | −6.24983 | + | 4.54076i | −0.251405 | + | 0.182656i | ||||
\(619\) | 11.0089 | + | 33.8820i | 0.442486 | + | 1.36183i | 0.885217 | + | 0.465178i | \(0.154010\pi\) |
−0.442731 | + | 0.896655i | \(0.645990\pi\) | |||||||
\(620\) | −3.98097 | + | 12.2522i | −0.159880 | + | 0.492059i | ||||
\(621\) | 5.70062 | + | 4.14175i | 0.228758 | + | 0.166203i | ||||
\(622\) | 5.64694 | + | 4.10274i | 0.226422 | + | 0.164505i | ||||
\(623\) | −7.79334 | + | 23.9854i | −0.312234 | + | 0.960956i | ||||
\(624\) | −5.44027 | − | 16.7434i | −0.217785 | − | 0.670273i | ||||
\(625\) | 25.2164 | − | 18.3208i | 1.00866 | − | 0.732831i | ||||
\(626\) | −86.0101 | −3.43766 | ||||||||
\(627\) | −1.45951 | − | 0.562008i | −0.0582871 | − | 0.0224444i | ||||
\(628\) | −53.4677 | −2.13359 | ||||||||
\(629\) | −0.139645 | + | 0.101458i | −0.00556800 | + | 0.00404539i | ||||
\(630\) | −9.84245 | − | 30.2919i | −0.392133 | − | 1.20686i | ||||
\(631\) | −1.66580 | + | 5.12680i | −0.0663144 | + | 0.204095i | −0.978723 | − | 0.205186i | \(-0.934220\pi\) |
0.912409 | + | 0.409280i | \(0.134220\pi\) | |||||||
\(632\) | −9.07225 | − | 6.59137i | −0.360875 | − | 0.262191i | ||||
\(633\) | −6.81043 | − | 4.94807i | −0.270690 | − | 0.196668i | ||||
\(634\) | −2.48836 | + | 7.65838i | −0.0988253 | + | 0.304153i | ||||
\(635\) | −18.5437 | − | 57.0717i | −0.735885 | − | 2.26482i | ||||
\(636\) | 59.7100 | − | 43.3818i | 2.36765 | − | 1.72020i | ||||
\(637\) | −9.80614 | −0.388533 | ||||||||
\(638\) | 15.7467 | − | 19.4039i | 0.623418 | − | 0.768209i | ||||
\(639\) | −14.6904 | −0.581144 | ||||||||
\(640\) | −143.862 | + | 104.522i | −5.68666 | + | 4.13160i | ||||
\(641\) | 10.0690 | + | 30.9891i | 0.397700 | + | 1.22399i | 0.926839 | + | 0.375459i | \(0.122515\pi\) |
−0.529139 | + | 0.848535i | \(0.677485\pi\) | |||||||
\(642\) | 4.90247 | − | 15.0883i | 0.193485 | − | 0.595486i | ||||
\(643\) | −4.88539 | − | 3.54945i | −0.192661 | − | 0.139976i | 0.487273 | − | 0.873250i | \(-0.337992\pi\) |
−0.679934 | + | 0.733273i | \(0.737992\pi\) | |||||||
\(644\) | −134.481 | − | 97.7065i | −5.29931 | − | 3.85017i | ||||
\(645\) | −3.23721 | + | 9.96310i | −0.127465 | + | 0.392297i | ||||
\(646\) | −0.218218 | − | 0.671605i | −0.00858566 | − | 0.0264240i | ||||
\(647\) | 28.8413 | − | 20.9544i | 1.13387 | − | 0.823804i | 0.147615 | − | 0.989045i | \(-0.452840\pi\) |
0.986253 | + | 0.165241i | \(0.0528403\pi\) | |||||||
\(648\) | −10.4550 | −0.410713 | ||||||||
\(649\) | −0.0201828 | + | 0.00538529i | −0.000792243 | + | 0.000211391i | ||||
\(650\) | 7.75347 | 0.304116 | ||||||||
\(651\) | 2.66123 | − | 1.93350i | 0.104302 | − | 0.0757797i | ||||
\(652\) | −40.4807 | − | 124.587i | −1.58535 | − | 4.87920i | ||||
\(653\) | −3.11773 | + | 9.59539i | −0.122006 | + | 0.375497i | −0.993344 | − | 0.115187i | \(-0.963253\pi\) |
0.871337 | + | 0.490684i | \(0.163253\pi\) | |||||||
\(654\) | 0.638062 | + | 0.463579i | 0.0249502 | + | 0.0181274i | ||||
\(655\) | 15.5282 | + | 11.2819i | 0.606737 | + | 0.440820i | ||||
\(656\) | 18.0312 | − | 55.4943i | 0.704000 | − | 2.16669i | ||||
\(657\) | −4.36333 | − | 13.4289i | −0.170230 | − | 0.523913i | ||||
\(658\) | 56.1802 | − | 40.8173i | 2.19013 | − | 1.59122i | ||||
\(659\) | −23.8252 | −0.928096 | −0.464048 | − | 0.885810i | \(-0.653604\pi\) | ||||
−0.464048 | + | 0.885810i | \(0.653604\pi\) | |||||||
\(660\) | 2.84257 | − | 53.1732i | 0.110647 | − | 2.06977i | ||||
\(661\) | 5.03023 | 0.195653 | 0.0978266 | − | 0.995203i | \(-0.468811\pi\) | ||||
0.0978266 | + | 0.995203i | \(0.468811\pi\) | |||||||
\(662\) | −30.3627 | + | 22.0598i | −1.18008 | + | 0.857377i | ||||
\(663\) | 0.166181 | + | 0.511452i | 0.00645393 | + | 0.0198632i | ||||
\(664\) | −5.69274 | + | 17.5205i | −0.220921 | + | 0.679926i | ||||
\(665\) | 4.36350 | + | 3.17027i | 0.169209 | + | 0.122938i | ||||
\(666\) | −0.723107 | − | 0.525368i | −0.0280198 | − | 0.0203576i | ||||
\(667\) | 5.89156 | − | 18.1324i | 0.228122 | − | 0.702088i | ||||
\(668\) | 12.5528 | + | 38.6336i | 0.485683 | + | 1.49478i | ||||
\(669\) | 12.5230 | − | 9.09851i | 0.484168 | − | 0.351769i | ||||
\(670\) | −32.2059 | −1.24422 | ||||||||
\(671\) | 1.74580 | − | 32.6570i | 0.0673958 | − | 1.26071i | ||||
\(672\) | 115.256 | 4.44611 | ||||||||
\(673\) | −6.61951 | + | 4.80935i | −0.255163 | + | 0.185387i | −0.708012 | − | 0.706200i | \(-0.750408\pi\) |
0.452849 | + | 0.891587i | \(0.350408\pi\) | |||||||
\(674\) | 18.5632 | + | 57.1317i | 0.715029 | + | 2.20063i | ||||
\(675\) | 0.860404 | − | 2.64805i | 0.0331169 | − | 0.101923i | ||||
\(676\) | −4.65547 | − | 3.38240i | −0.179057 | − | 0.130092i | ||||
\(677\) | −35.8450 | − | 26.0429i | −1.37763 | − | 1.00091i | −0.997097 | − | 0.0761442i | \(-0.975739\pi\) |
−0.380537 | − | 0.924766i | \(-0.624261\pi\) | |||||||
\(678\) | −0.478852 | + | 1.47375i | −0.0183902 | + | 0.0565992i | ||||
\(679\) | −4.58526 | − | 14.1120i | −0.175966 | − | 0.541568i | ||||
\(680\) | 12.6909 | − | 9.22049i | 0.486674 | − | 0.353589i | ||||
\(681\) | 5.32988 | 0.204242 | ||||||||
\(682\) | 7.16026 | − | 1.91055i | 0.274180 | − | 0.0731586i | ||||
\(683\) | 4.88202 | 0.186805 | 0.0934026 | − | 0.995628i | \(-0.470226\pi\) | ||||
0.0934026 | + | 0.995628i | \(0.470226\pi\) | |||||||
\(684\) | 2.19531 | − | 1.59499i | 0.0839399 | − | 0.0609859i | ||||
\(685\) | −10.6817 | − | 32.8750i | −0.408128 | − | 1.25609i | ||||
\(686\) | 9.89924 | − | 30.4667i | 0.377955 | − | 1.16323i | ||||
\(687\) | −15.0117 | − | 10.9066i | −0.572732 | − | 0.416114i | ||||
\(688\) | −53.4778 | − | 38.8539i | −2.03882 | − | 1.48129i | ||||
\(689\) | 3.96338 | − | 12.1980i | 0.150993 | − | 0.464708i | ||||
\(690\) | −16.9174 | − | 52.0664i | −0.644035 | − | 1.98214i | ||||
\(691\) | 11.4661 | − | 8.33063i | 0.436192 | − | 0.316912i | −0.347928 | − | 0.937521i | \(-0.613115\pi\) |
0.784120 | + | 0.620609i | \(0.213115\pi\) | |||||||
\(692\) | −45.8634 | −1.74347 | ||||||||
\(693\) | −8.56769 | + | 10.5576i | −0.325459 | + | 0.401049i | ||||
\(694\) | −77.2390 | −2.93195 | ||||||||
\(695\) | −39.5004 | + | 28.6987i | −1.49833 | + | 1.08860i | ||||
\(696\) | 8.74162 | + | 26.9039i | 0.331350 | + | 1.01979i | ||||
\(697\) | −0.550789 | + | 1.69516i | −0.0208626 | + | 0.0642086i | ||||
\(698\) | 26.2402 | + | 19.0646i | 0.993205 | + | 0.721606i | ||||
\(699\) | −10.6364 | − | 7.72780i | −0.402306 | − | 0.292292i | ||||
\(700\) | −20.2975 | + | 62.4692i | −0.767173 | + | 2.36111i | ||||
\(701\) | −8.79806 | − | 27.0777i | −0.332298 | − | 1.02271i | −0.968038 | − | 0.250805i | \(-0.919305\pi\) |
0.635739 | − | 0.771904i | \(-0.280695\pi\) | |||||||
\(702\) | −2.25286 | + | 1.63680i | −0.0850287 | + | 0.0617769i | ||||
\(703\) | 0.151357 | 0.00570852 | ||||||||
\(704\) | 133.336 | + | 51.3434i | 5.02530 | + | 1.93508i | ||||
\(705\) | 16.9717 | 0.639192 | ||||||||
\(706\) | 52.4259 | − | 38.0897i | 1.97308 | − | 1.43352i | ||||
\(707\) | 16.5384 | + | 50.8998i | 0.621989 | + | 1.91429i | ||||
\(708\) | 0.0111997 | − | 0.0344692i | 0.000420911 | − | 0.00129543i | ||||
\(709\) | −21.3030 | − | 15.4776i | −0.800052 | − | 0.581272i | 0.110877 | − | 0.993834i | \(-0.464634\pi\) |
−0.910929 | + | 0.412562i | \(0.864634\pi\) | |||||||
\(710\) | 92.3377 | + | 67.0872i | 3.46537 | + | 2.51774i | ||||
\(711\) | −0.331447 | + | 1.02009i | −0.0124302 | + | 0.0382563i | ||||
\(712\) | −19.8754 | − | 61.1702i | −0.744862 | − | 2.29245i | ||||
\(713\) | 4.57418 | − | 3.32333i | 0.171304 | − | 0.124460i | ||||
\(714\) | −6.13916 | −0.229752 | ||||||||
\(715\) | −5.03169 | − | 7.76593i | −0.188175 | − | 0.290429i | ||||
\(716\) | −78.6254 | −2.93837 | ||||||||
\(717\) | −18.5380 | + | 13.4686i | −0.692313 | + | 0.502995i | ||||
\(718\) | 25.6707 | + | 79.0062i | 0.958021 | + | 2.94849i | ||||
\(719\) | 8.31147 | − | 25.5801i | 0.309965 | − | 0.953976i | −0.667812 | − | 0.744330i | \(-0.732769\pi\) |
0.977777 | − | 0.209646i | \(-0.0672310\pi\) | |||||||
\(720\) | 39.7380 | + | 28.8713i | 1.48095 | + | 1.07597i | ||||
\(721\) | −9.20080 | − | 6.68477i | −0.342656 | − | 0.248954i | ||||
\(722\) | 16.1584 | − | 49.7306i | 0.601355 | − | 1.85078i | ||||
\(723\) | 3.83560 | + | 11.8048i | 0.142647 | + | 0.439024i | ||||
\(724\) | −31.0637 | + | 22.5691i | −1.15447 | + | 0.838775i | ||||
\(725\) | −7.53361 | −0.279791 | ||||||||
\(726\) | −26.5597 | + | 15.2601i | −0.985725 | + | 0.566357i | ||||
\(727\) | −17.4868 | −0.648550 | −0.324275 | − | 0.945963i | \(-0.605120\pi\) | ||||
−0.324275 | + | 0.945963i | \(0.605120\pi\) | |||||||
\(728\) | 34.6751 | − | 25.1929i | 1.28514 | − | 0.933712i | ||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | −33.9004 | + | 104.335i | −1.25471 | + | 3.86160i | ||||
\(731\) | 1.63356 | + | 1.18685i | 0.0604193 | + | 0.0438972i | ||||
\(732\) | 45.9053 | + | 33.3521i | 1.69671 | + | 1.23273i | ||||
\(733\) | −14.6925 | + | 45.2188i | −0.542679 | + | 1.67019i | 0.183767 | + | 0.982970i | \(0.441171\pi\) |
−0.726446 | + | 0.687224i | \(0.758829\pi\) | |||||||
\(734\) | 7.95049 | + | 24.4691i | 0.293458 | + | 0.903171i | ||||
\(735\) | 22.1343 | − | 16.0815i | 0.816437 | − | 0.593176i | ||||
\(736\) | 198.105 | 7.30224 | ||||||||
\(737\) | 7.47570 | + | 11.5380i | 0.275371 | + | 0.425008i | ||||
\(738\) | −9.22956 | −0.339745 | ||||||||
\(739\) | 20.3949 | − | 14.8178i | 0.750239 | − | 0.545081i | −0.145662 | − | 0.989334i | \(-0.546531\pi\) |
0.895901 | + | 0.444254i | \(0.146531\pi\) | |||||||
\(740\) | 1.59246 | + | 4.90107i | 0.0585398 | + | 0.180167i | ||||
\(741\) | 0.145719 | − | 0.448476i | 0.00535311 | − | 0.0164752i | ||||
\(742\) | 118.454 | + | 86.0621i | 4.34860 | + | 3.15944i | ||||
\(743\) | 10.3196 | + | 7.49763i | 0.378589 | + | 0.275061i | 0.760764 | − | 0.649029i | \(-0.224825\pi\) |
−0.382174 | + | 0.924090i | \(0.624825\pi\) | |||||||
\(744\) | −2.59238 | + | 7.97853i | −0.0950413 | + | 0.292507i | ||||
\(745\) | 7.37422 | + | 22.6955i | 0.270170 | + | 0.831499i | ||||
\(746\) | 21.3024 | − | 15.4771i | 0.779938 | − | 0.566658i | ||||
\(747\) | 1.76203 | 0.0644693 | ||||||||
\(748\) | −9.57806 | − | 3.68820i | −0.350209 | − | 0.134854i | ||||
\(749\) | 23.3556 | 0.853394 | ||||||||
\(750\) | 13.9268 | − | 10.1184i | 0.508534 | − | 0.369472i | ||||
\(751\) | −9.61804 | − | 29.6013i | −0.350967 | − | 1.08017i | −0.958311 | − | 0.285727i | \(-0.907765\pi\) |
0.607344 | − | 0.794439i | \(-0.292235\pi\) | |||||||
\(752\) | −33.0929 | + | 101.850i | −1.20678 | + | 3.71407i | ||||
\(753\) | −4.67644 | − | 3.39763i | −0.170419 | − | 0.123817i | ||||
\(754\) | 6.09561 | + | 4.42872i | 0.221989 | + | 0.161285i | ||||
\(755\) | −10.1536 | + | 31.2495i | −0.369526 | + | 1.13729i | ||||
\(756\) | −7.28991 | − | 22.4360i | −0.265132 | − | 0.815991i | ||||
\(757\) | −6.60370 | + | 4.79787i | −0.240015 | + | 0.174381i | −0.701290 | − | 0.712876i | \(-0.747392\pi\) |
0.461275 | + | 0.887257i | \(0.347392\pi\) | |||||||
\(758\) | −31.7598 | −1.15357 | ||||||||
\(759\) | −14.7263 | + | 18.1466i | −0.534532 | + | 0.658679i | ||||
\(760\) | −13.7553 | −0.498956 | ||||||||
\(761\) | −19.6793 | + | 14.2978i | −0.713374 | + | 0.518296i | −0.884260 | − | 0.466994i | \(-0.845337\pi\) |
0.170886 | + | 0.985291i | \(0.445337\pi\) | |||||||
\(762\) | −18.5081 | − | 56.9622i | −0.670479 | − | 2.06352i | ||||
\(763\) | −0.358794 | + | 1.10426i | −0.0129892 | + | 0.0399767i | ||||
\(764\) | −83.0255 | − | 60.3215i | −3.00376 | − | 2.18236i | ||||
\(765\) | −1.21385 | − | 0.881917i | −0.0438870 | − | 0.0318858i | ||||
\(766\) | 30.7611 | − | 94.6730i | 1.11144 | − | 3.42067i | ||||
\(767\) | −0.00194626 | − | 0.00598998i | −7.02754e−5 | − | 0.000216286i | ||||
\(768\) | −73.8815 | + | 53.6780i | −2.66597 | + | 1.93694i | ||||
\(769\) | −15.0974 | −0.544427 | −0.272214 | − | 0.962237i | \(-0.587756\pi\) | ||||
−0.272214 | + | 0.962237i | \(0.587756\pi\) | |||||||
\(770\) | 102.066 | − | 27.2340i | 3.67822 | − | 0.981445i | ||||
\(771\) | −15.9866 | −0.575745 | ||||||||
\(772\) | −66.2361 | + | 48.1233i | −2.38389 | + | 1.73200i | ||||
\(773\) | −12.7060 | − | 39.1051i | −0.457004 | − | 1.40651i | −0.868767 | − | 0.495221i | \(-0.835087\pi\) |
0.411763 | − | 0.911291i | \(-0.364913\pi\) | |||||||
\(774\) | −3.23100 | + | 9.94399i | −0.116136 | + | 0.357429i | ||||
\(775\) | −1.80746 | − | 1.31319i | −0.0649258 | − | 0.0471713i | ||||
\(776\) | 30.6148 | + | 22.2429i | 1.09901 | + | 0.798475i | ||||
\(777\) | 0.406616 | − | 1.25144i | 0.0145873 | − | 0.0448950i | ||||
\(778\) | 9.44880 | + | 29.0804i | 0.338756 | + | 1.04258i | ||||
\(779\) | 1.26443 | − | 0.918663i | 0.0453029 | − | 0.0329145i | ||||
\(780\) | 16.0552 | 0.574869 | ||||||||
\(781\) | 2.60093 | − | 48.6532i | 0.0930688 | − | 1.74095i | ||||
\(782\) | −10.5521 | −0.377343 | ||||||||
\(783\) | 2.18898 | − | 1.59038i | 0.0782276 | − | 0.0568357i | ||||
\(784\) | 53.3480 | + | 164.188i | 1.90529 | + | 5.86387i | ||||
\(785\) | 8.01084 | − | 24.6548i | 0.285919 | − | 0.879969i | ||||
\(786\) | 15.4984 | + | 11.2602i | 0.552810 | + | 0.401640i | ||||
\(787\) | 12.9819 | + | 9.43187i | 0.462753 | + | 0.336210i | 0.794610 | − | 0.607120i | \(-0.207675\pi\) |
−0.331857 | + | 0.943330i | \(0.607675\pi\) | |||||||
\(788\) | 24.9599 | − | 76.8188i | 0.889161 | − | 2.73655i | ||||
\(789\) | −1.39842 | − | 4.30389i | −0.0497851 | − | 0.153223i | ||||
\(790\) | 6.74180 | − | 4.89820i | 0.239862 | − | 0.174270i | ||||
\(791\) | −2.28127 | −0.0811126 | ||||||||
\(792\) | 1.85106 | − | 34.6260i | 0.0657746 | − | 1.23038i | ||||
\(793\) | 9.86050 | 0.350157 | ||||||||
\(794\) | −19.6365 | + | 14.2667i | −0.696872 | + | 0.506307i | ||||
\(795\) | 11.0580 | + | 34.0330i | 0.392186 | + | 1.20703i | ||||
\(796\) | 7.97826 | − | 24.5545i | 0.282782 | − | 0.870313i | ||||
\(797\) | −9.17494 | − | 6.66599i | −0.324993 | − | 0.236121i | 0.413310 | − | 0.910590i | \(-0.364373\pi\) |
−0.738303 | + | 0.674469i | \(0.764373\pi\) | |||||||
\(798\) | 4.35513 | + | 3.16418i | 0.154170 | + | 0.112011i | ||||
\(799\) | 1.01087 | − | 3.11114i | 0.0357621 | − | 0.110064i | ||||
\(800\) | −24.1898 | − | 74.4486i | −0.855239 | − | 2.63216i | ||||
\(801\) | −4.97697 | + | 3.61598i | −0.175853 | + | 0.127764i | ||||
\(802\) | −92.9074 | −3.28068 | ||||||||
\(803\) | 45.2478 | − | 12.0733i | 1.59676 | − | 0.426058i | ||||
\(804\) | −23.8536 | −0.841252 | ||||||||
\(805\) | 65.2029 | − | 47.3727i | 2.29810 | − | 1.66967i | ||||
\(806\) | 0.690477 | + | 2.12507i | 0.0243210 | + | 0.0748524i | ||||
\(807\) | 1.80888 | − | 5.56717i | 0.0636757 | − | 0.195974i | ||||
\(808\) | −110.423 | − | 80.2271i | −3.88467 | − | 2.82238i | ||||
\(809\) | −20.7855 | − | 15.1015i | −0.730778 | − | 0.530941i | 0.159031 | − | 0.987274i | \(-0.449163\pi\) |
−0.889809 | + | 0.456332i | \(0.849163\pi\) | |||||||
\(810\) | 2.40087 | − | 7.38913i | 0.0843581 | − | 0.259627i | ||||
\(811\) | 7.34603 | + | 22.6087i | 0.257954 | + | 0.793901i | 0.993233 | + | 0.116136i | \(0.0370510\pi\) |
−0.735279 | + | 0.677764i | \(0.762949\pi\) | |||||||
\(812\) | −51.6394 | + | 37.5182i | −1.81219 | + | 1.31663i | ||||
\(813\) | −14.0384 | −0.492350 | ||||||||
\(814\) | 1.86799 | − | 2.30184i | 0.0654730 | − | 0.0806794i | ||||
\(815\) | 63.5141 | 2.22480 | ||||||||
\(816\) | 7.65939 | − | 5.56487i | 0.268132 | − | 0.194809i | ||||
\(817\) | −0.547133 | − | 1.68390i | −0.0191418 | − | 0.0589123i | ||||
\(818\) | 28.8519 | − | 88.7970i | 1.00878 | − | 3.10472i | ||||
\(819\) | −3.31659 | − | 2.40964i | −0.115891 | − | 0.0841997i | ||||
\(820\) | 43.0505 | + | 31.2780i | 1.50339 | + | 1.09228i | ||||
\(821\) | 7.09436 | − | 21.8342i | 0.247595 | − | 0.762019i | −0.747604 | − | 0.664145i | \(-0.768796\pi\) |
0.995199 | − | 0.0978738i | \(-0.0312042\pi\) | |||||||
\(822\) | −10.6612 | − | 32.8119i | −0.371854 | − | 1.14445i | ||||
\(823\) | 7.57934 | − | 5.50671i | 0.264199 | − | 0.191952i | −0.447797 | − | 0.894135i | \(-0.647791\pi\) |
0.711996 | + | 0.702183i | \(0.247791\pi\) | |||||||
\(824\) | 29.0041 | 1.01041 | ||||||||
\(825\) | 8.61773 | + | 3.31840i | 0.300031 | + | 0.115532i | ||||
\(826\) | 0.0719000 | 0.00250172 | ||||||||
\(827\) | −20.2809 | + | 14.7349i | −0.705235 | + | 0.512383i | −0.881633 | − | 0.471936i | \(-0.843555\pi\) |
0.176398 | + | 0.984319i | \(0.443555\pi\) | |||||||
\(828\) | −12.5301 | − | 38.5636i | −0.435450 | − | 1.34018i | ||||
\(829\) | 2.08322 | − | 6.41150i | 0.0723533 | − | 0.222681i | −0.908340 | − | 0.418232i | \(-0.862650\pi\) |
0.980693 | + | 0.195552i | \(0.0626498\pi\) | |||||||
\(830\) | −11.0754 | − | 8.04672i | −0.384431 | − | 0.279306i | ||||
\(831\) | −4.57455 | − | 3.32361i | −0.158689 | − | 0.115295i | ||||
\(832\) | −13.3124 | + | 40.9715i | −0.461526 | + | 1.42043i | ||||
\(833\) | −1.62959 | − | 5.01537i | −0.0564620 | − | 0.173772i | ||||
\(834\) | −39.4246 | + | 28.6436i | −1.36516 | + | 0.991847i | ||||
\(835\) | −19.6953 | −0.681584 | ||||||||
\(836\) | 4.89376 | + | 7.55304i | 0.169254 | + | 0.261227i | ||||
\(837\) | 0.802399 | 0.0277350 | ||||||||
\(838\) | 18.6107 | − | 13.5215i | 0.642896 | − | 0.467092i | ||||
\(839\) | 13.8118 | + | 42.5085i | 0.476838 | + | 1.46756i | 0.843463 | + | 0.537187i | \(0.180513\pi\) |
−0.366625 | + | 0.930369i | \(0.619487\pi\) | |||||||
\(840\) | −36.9533 | + | 113.730i | −1.27501 | + | 3.92407i | ||||
\(841\) | 17.5387 | + | 12.7426i | 0.604784 | + | 0.439401i | ||||
\(842\) | −16.0620 | − | 11.6697i | −0.553533 | − | 0.402165i | ||||
\(843\) | −6.45427 | + | 19.8642i | −0.222297 | + | 0.684159i | ||||
\(844\) | 14.9694 | + | 46.0712i | 0.515269 | + | 1.58584i | ||||
\(845\) | 2.25719 | − | 1.63994i | 0.0776497 | − | 0.0564158i | ||||
\(846\) | 16.9391 | 0.582380 | ||||||||
\(847\) | −33.4487 | − | 30.2445i | −1.14931 | − | 1.03921i | ||||
\(848\) | −225.798 | −7.75395 | ||||||||
\(849\) | −16.0717 | + | 11.6767i | −0.551578 | + | 0.400745i | ||||
\(850\) | 1.28848 | + | 3.96553i | 0.0441944 | + | 0.136017i | ||||
\(851\) | 0.698901 | − | 2.15100i | 0.0239580 | − | 0.0737352i | ||||
\(852\) | 68.3909 | + | 49.6889i | 2.34303 | + | 1.70231i | ||||
\(853\) | −17.3639 | − | 12.6156i | −0.594528 | − | 0.431950i | 0.249405 | − | 0.968399i | \(-0.419765\pi\) |
−0.843932 | + | 0.536450i | \(0.819765\pi\) | |||||||
\(854\) | −34.7850 | + | 107.057i | −1.19032 | + | 3.66342i | ||||
\(855\) | 0.406561 | + | 1.25127i | 0.0139041 | + | 0.0427924i | ||||
\(856\) | −48.1881 | + | 35.0107i | −1.64704 | + | 1.19664i | ||||
\(857\) | −8.46288 | −0.289087 | −0.144543 | − | 0.989498i | \(-0.546171\pi\) | ||||
−0.144543 | + | 0.989498i | \(0.546171\pi\) | |||||||
\(858\) | −5.02204 | − | 7.75103i | −0.171449 | − | 0.264616i | ||||
\(859\) | −32.1582 | −1.09722 | −0.548611 | − | 0.836078i | \(-0.684843\pi\) | ||||
−0.548611 | + | 0.836078i | \(0.684843\pi\) | |||||||
\(860\) | 48.7699 | − | 35.4334i | 1.66304 | − | 1.20827i | ||||
\(861\) | −4.19876 | − | 12.9224i | −0.143093 | − | 0.440396i | ||||
\(862\) | 21.5226 | − | 66.2399i | 0.733064 | − | 2.25614i | ||||
\(863\) | −13.1749 | − | 9.57215i | −0.448480 | − | 0.325840i | 0.340515 | − | 0.940239i | \(-0.389398\pi\) |
−0.788995 | + | 0.614399i | \(0.789398\pi\) | |||||||
\(864\) | 22.7451 | + | 16.5253i | 0.773805 | + | 0.562202i | ||||
\(865\) | 6.87153 | − | 21.1484i | 0.233639 | − | 0.719066i | ||||
\(866\) | 11.2910 | + | 34.7500i | 0.383683 | + | 1.18085i | ||||
\(867\) | 13.5193 | − | 9.82236i | 0.459140 | − | 0.333585i | ||||
\(868\) | −18.9291 | −0.642496 | ||||||||
\(869\) | −3.31974 | − | 1.27832i | −0.112615 | − | 0.0433641i | ||||
\(870\) | −21.0218 | −0.712706 | ||||||||
\(871\) | −3.35356 | + | 2.43650i | −0.113631 | + | 0.0825577i | ||||
\(872\) | −0.915035 | − | 2.81619i | −0.0309870 | − | 0.0953681i | ||||
\(873\) | 1.11848 | − | 3.44234i | 0.0378550 | − | 0.116506i | ||||
\(874\) | 7.48568 | + | 5.43867i | 0.253207 | + | 0.183966i | ||||
\(875\) | 20.5026 | + | 14.8960i | 0.693113 | + | 0.503576i | ||||
\(876\) | −25.1087 | + | 77.2766i | −0.848344 | + | 2.61093i | ||||
\(877\) | 4.20103 | + | 12.9295i | 0.141859 | + | 0.436597i | 0.996594 | − | 0.0824682i | \(-0.0262803\pi\) |
−0.854735 | + | 0.519065i | \(0.826280\pi\) | |||||||
\(878\) | −52.4177 | + | 38.0837i | −1.76901 | + | 1.28526i | ||||
\(879\) | 29.7117 | 1.00215 | ||||||||
\(880\) | −102.654 | + | 126.496i | −3.46048 | + | 4.26419i | ||||
\(881\) | −27.4177 | −0.923725 | −0.461862 | − | 0.886952i | \(-0.652819\pi\) | ||||
−0.461862 | + | 0.886952i | \(0.652819\pi\) | |||||||
\(882\) | 22.0918 | − | 16.0507i | 0.743871 | − | 0.540454i | ||||
\(883\) | 6.52446 | + | 20.0802i | 0.219566 | + | 0.675753i | 0.998798 | + | 0.0490181i | \(0.0156092\pi\) |
−0.779232 | + | 0.626735i | \(0.784391\pi\) | |||||||
\(884\) | 0.956284 | − | 2.94314i | 0.0321633 | − | 0.0989885i | ||||
\(885\) | 0.0142163 | + | 0.0103288i | 0.000477876 | + | 0.000347197i | ||||
\(886\) | 73.9219 | + | 53.7074i | 2.48345 | + | 1.80434i | ||||
\(887\) | −6.19632 | + | 19.0703i | −0.208052 | + | 0.640318i | 0.791522 | + | 0.611140i | \(0.209289\pi\) |
−0.999574 | + | 0.0291780i | \(0.990711\pi\) | |||||||
\(888\) | 1.03700 | + | 3.19154i | 0.0347993 | + | 0.107101i | ||||
\(889\) | 71.3339 | − | 51.8271i | 2.39246 | − | 1.73822i | ||||
\(890\) | 47.7963 | 1.60213 | ||||||||
\(891\) | −3.20451 | + | 0.855048i | −0.107355 | + | 0.0286452i | ||||
\(892\) | −89.0754 | −2.98247 | ||||||||
\(893\) | −2.32063 | + | 1.68604i | −0.0776569 | + | 0.0564210i | ||||
\(894\) | 7.36007 | + | 22.6520i | 0.246157 | + | 0.757595i | ||||
\(895\) | 11.7801 | − | 36.2555i | 0.393766 | − | 1.21189i | ||||
\(896\) | −211.383 | − | 153.579i | −7.06182 | − | 5.13071i | ||||
\(897\) | −5.70062 | − | 4.14175i | −0.190338 | − | 0.138289i | ||||
\(898\) | −15.3971 | + | 47.3874i | −0.513808 | + | 1.58134i | ||||
\(899\) | −0.670898 | − | 2.06481i | −0.0223757 | − | 0.0688653i | ||||
\(900\) | −12.9623 | + | 9.41769i | −0.432078 | + | 0.313923i | ||||
\(901\) | 6.89734 | 0.229784 | ||||||||
\(902\) | 1.63409 | − | 30.5673i | 0.0544092 | − | 1.01778i | ||||
\(903\) | −15.3926 | −0.512234 | ||||||||
\(904\) | 4.70680 | − | 3.41969i | 0.156546 | − | 0.113737i | ||||
\(905\) | −5.75284 | − | 17.7054i | −0.191231 | − | 0.588549i | ||||
\(906\) | −10.1341 | + | 31.1895i | −0.336683 | + | 1.03620i | ||||
\(907\) | −12.1177 | − | 8.80400i | −0.402360 | − | 0.292332i | 0.368141 | − | 0.929770i | \(-0.379994\pi\) |
−0.770502 | + | 0.637438i | \(0.779994\pi\) | |||||||
\(908\) | −24.8131 | − | 18.0278i | −0.823452 | − | 0.598273i | ||||
\(909\) | −4.03421 | + | 12.4160i | −0.133806 | + | 0.411813i | ||||
\(910\) | 9.84245 | + | 30.2919i | 0.326274 | + | 1.00417i | ||||
\(911\) | −30.3517 | + | 22.0518i | −1.00560 | + | 0.730609i | −0.963281 | − | 0.268495i | \(-0.913474\pi\) |
−0.0423165 | + | 0.999104i | \(0.513474\pi\) | |||||||
\(912\) | −8.30177 | −0.274899 | ||||||||
\(913\) | −0.311967 | + | 5.83566i | −0.0103246 | + | 0.193132i | ||||
\(914\) | 60.7171 | 2.00834 | ||||||||
\(915\) | −22.2570 | + | 16.1707i | −0.735795 | + | 0.534586i | ||||
\(916\) | 32.9960 | + | 101.551i | 1.09022 | + | 3.35534i | ||||
\(917\) | −8.71504 | + | 26.8221i | −0.287796 | + | 0.885745i | ||||
\(918\) | −1.21153 | − | 0.880225i | −0.0399863 | − | 0.0290517i | ||||
\(919\) | −20.9454 | − | 15.2177i | −0.690924 | − | 0.501986i | 0.186039 | − | 0.982542i | \(-0.440435\pi\) |
−0.876964 | + | 0.480556i | \(0.840435\pi\) | |||||||
\(920\) | −63.5161 | + | 195.482i | −2.09406 | + | 6.44486i | ||||
\(921\) | −2.99840 | − | 9.22812i | −0.0988006 | − | 0.304077i | ||||
\(922\) | 34.7152 | − | 25.2221i | 1.14328 | − | 0.830645i | ||||
\(923\) | 14.6904 | 0.483541 | ||||||||
\(924\) | 75.5965 | − | 20.1711i | 2.48694 | − | 0.663582i | ||||
\(925\) | −0.893693 | −0.0293844 | ||||||||
\(926\) | 70.4226 | − | 51.1650i | 2.31423 | − | 1.68139i | ||||
\(927\) | −0.857268 | − | 2.63840i | −0.0281564 | − | 0.0866564i | ||||
\(928\) | 23.5070 | − | 72.3470i | 0.771654 | − | 2.37491i | ||||
\(929\) | −39.7104 | − | 28.8513i | −1.30286 | − | 0.946581i | −0.302878 | − | 0.953029i | \(-0.597947\pi\) |
−0.999979 | + | 0.00644820i | \(0.997947\pi\) | |||||||
\(930\) | −5.04353 | − | 3.66434i | −0.165384 | − | 0.120159i | ||||
\(931\) | −1.42894 | + | 4.39782i | −0.0468315 | + | 0.144133i | ||||
\(932\) | 23.3790 | + | 71.9531i | 0.765804 | + | 2.35690i | ||||
\(933\) | −2.02785 | + | 1.47332i | −0.0663890 | + | 0.0482344i | ||||
\(934\) | 36.6816 | 1.20026 | ||||||||
\(935\) | 3.13573 | − | 3.86402i | 0.102549 | − | 0.126367i | ||||
\(936\) | 10.4550 | 0.341734 | ||||||||
\(937\) | 28.4120 | − | 20.6425i | 0.928179 | − | 0.674361i | −0.0173675 | − | 0.999849i | \(-0.505529\pi\) |
0.945546 | + | 0.325488i | \(0.105529\pi\) | |||||||
\(938\) | −14.6231 | − | 45.0054i | −0.477463 | − | 1.46948i | ||||
\(939\) | 9.54455 | − | 29.3751i | 0.311475 | − | 0.958621i | ||||
\(940\) | −79.0113 | − | 57.4051i | −2.57707 | − | 1.87235i | ||||
\(941\) | 25.7924 | + | 18.7393i | 0.840809 | + | 0.610884i | 0.922597 | − | 0.385766i | \(-0.126063\pi\) |
−0.0817873 | + | 0.996650i | \(0.526063\pi\) | |||||||
\(942\) | 7.99547 | − | 24.6075i | 0.260506 | − | 0.801757i | ||||
\(943\) | −7.21691 | − | 22.2114i | −0.235015 | − | 0.723302i | ||||
\(944\) | −0.0897045 | + | 0.0651741i | −0.00291963 | + | 0.00212124i | ||||
\(945\) | 11.4379 | 0.372073 | ||||||||
\(946\) | −32.3614 | − | 12.4613i | −1.05216 | − | 0.405152i | ||||
\(947\) | 19.2891 | 0.626810 | 0.313405 | − | 0.949620i | \(-0.398530\pi\) | ||||
0.313405 | + | 0.949620i | \(0.398530\pi\) | |||||||
\(948\) | 4.99338 | − | 3.62790i | 0.162178 | − | 0.117829i | ||||
\(949\) | 4.36333 | + | 13.4289i | 0.141640 | + | 0.435922i | ||||
\(950\) | 1.12983 | − | 3.47725i | 0.0366564 | − | 0.112817i | ||||
\(951\) | −2.33944 | − | 1.69970i | −0.0758615 | − | 0.0551166i | ||||
\(952\) | 18.6473 | + | 13.5481i | 0.604363 | + | 0.439095i | ||||
\(953\) | −8.18792 | + | 25.1998i | −0.265233 | + | 0.816303i | 0.726407 | + | 0.687265i | \(0.241189\pi\) |
−0.991640 | + | 0.129038i | \(0.958811\pi\) | |||||||
\(954\) | 11.0368 | + | 33.9677i | 0.357328 | + | 1.09974i | ||||
\(955\) | 40.2546 | − | 29.2467i | 1.30261 | − | 0.946401i | ||||
\(956\) | 131.859 | 4.26463 | ||||||||
\(957\) | 4.87963 | + | 7.53124i | 0.157736 | + | 0.243450i | ||||
\(958\) | −34.9575 | −1.12943 | ||||||||
\(959\) | 41.0905 | − | 29.8540i | 1.32688 | − | 0.964035i | ||||
\(960\) | −37.1422 | − | 114.312i | −1.19876 | − | 3.68941i | ||||
\(961\) | −9.38057 | + | 28.8704i | −0.302599 | + | 0.931304i | ||||
\(962\) | 0.723107 | + | 0.525368i | 0.0233139 | + | 0.0169385i | ||||
\(963\) | 4.60908 | + | 3.34869i | 0.148525 | + | 0.107910i | ||||
\(964\) | 22.0719 | − | 67.9302i | 0.710887 | − | 2.18789i | ||||
\(965\) | −12.2666 | − | 37.7527i | −0.394875 | − | 1.21530i | ||||
\(966\) | 65.0778 | − | 47.2818i | 2.09384 | − | 1.52127i | ||||
\(967\) | −30.5524 | −0.982500 | −0.491250 | − | 0.871019i | \(-0.663460\pi\) | ||||
−0.491250 | + | 0.871019i | \(0.663460\pi\) | |||||||
\(968\) | 114.350 | + | 12.2610i | 3.67535 | + | 0.394085i | ||||
\(969\) | 0.253590 | 0.00814647 | ||||||||
\(970\) | −22.7506 | + | 16.5292i | −0.730476 | + | 0.530722i | ||||
\(971\) | −15.0123 | − | 46.2031i | −0.481767 | − | 1.48273i | −0.836609 | − | 0.547800i | \(-0.815465\pi\) |
0.354842 | − | 0.934926i | \(-0.384535\pi\) | |||||||
\(972\) | 1.77823 | − | 5.47283i | 0.0570368 | − | 0.175541i | ||||
\(973\) | −58.0396 | − | 42.1683i | −1.86066 | − | 1.35185i | ||||
\(974\) | 17.7972 | + | 12.9304i | 0.570260 | + | 0.414318i | ||||
\(975\) | −0.860404 | + | 2.64805i | −0.0275550 | + | 0.0848055i | ||||
\(976\) | −53.6438 | − | 165.099i | −1.71710 | − | 5.28468i | ||||
\(977\) | −11.9217 | + | 8.66160i | −0.381408 | + | 0.277109i | −0.761926 | − | 0.647665i | \(-0.775746\pi\) |
0.380518 | + | 0.924774i | \(0.375746\pi\) | |||||||
\(978\) | 63.3923 | 2.02706 | ||||||||
\(979\) | −11.0946 | − | 17.1234i | −0.354584 | − | 0.547266i | ||||
\(980\) | −157.440 | −5.02923 | ||||||||
\(981\) | −0.229133 | + | 0.166475i | −0.00731564 | + | 0.00531512i | ||||
\(982\) | 1.76272 | + | 5.42508i | 0.0562505 | + | 0.173121i | ||||
\(983\) | 12.5558 | − | 38.6427i | 0.400467 | − | 1.23251i | −0.524155 | − | 0.851623i | \(-0.675619\pi\) |
0.924622 | − | 0.380887i | \(-0.124381\pi\) | |||||||
\(984\) | 28.0342 | + | 20.3680i | 0.893698 | + | 0.649309i | ||||
\(985\) | 31.6828 | + | 23.0189i | 1.00950 | + | 0.733442i | ||||
\(986\) | −1.25211 | + | 3.85358i | −0.0398751 | + | 0.122723i | ||||
\(987\) | 7.70605 | + | 23.7168i | 0.245286 | + | 0.754913i | ||||
\(988\) | −2.19531 | + | 1.59499i | −0.0698422 | + | 0.0507433i | ||||
\(989\) | −26.4571 | −0.841288 | ||||||||
\(990\) | 24.0469 | + | 9.25968i | 0.764262 | + | 0.294292i | ||||
\(991\) | 55.7863 | 1.77211 | 0.886056 | − | 0.463579i | \(-0.153435\pi\) | ||||
0.886056 | + | 0.463579i | \(0.153435\pi\) | |||||||
\(992\) | 18.2507 | − | 13.2599i | 0.579459 | − | 0.421002i | ||||
\(993\) | −4.16474 | − | 12.8178i | −0.132164 | − | 0.406760i | ||||
\(994\) | −51.8235 | + | 159.496i | −1.64374 | + | 5.05892i | ||||
\(995\) | 10.1272 | + | 7.35781i | 0.321053 | + | 0.233258i | ||||
\(996\) | −8.20308 | − | 5.95989i | −0.259925 | − | 0.188846i | ||||
\(997\) | −5.51651 | + | 16.9781i | −0.174709 | + | 0.537700i | −0.999620 | − | 0.0275627i | \(-0.991225\pi\) |
0.824911 | + | 0.565263i | \(0.191225\pi\) | |||||||
\(998\) | 22.1501 | + | 68.1711i | 0.701150 | + | 2.15792i | ||||
\(999\) | 0.259673 | − | 0.188663i | 0.00821568 | − | 0.00596904i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 429.2.n.d.157.9 | ✓ | 36 | |
11.2 | odd | 10 | 4719.2.a.br.1.18 | 18 | |||
11.4 | even | 5 | inner | 429.2.n.d.235.9 | yes | 36 | |
11.9 | even | 5 | 4719.2.a.bq.1.1 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.n.d.157.9 | ✓ | 36 | 1.1 | even | 1 | trivial | |
429.2.n.d.235.9 | yes | 36 | 11.4 | even | 5 | inner | |
4719.2.a.bq.1.1 | 18 | 11.9 | even | 5 | |||
4719.2.a.br.1.18 | 18 | 11.2 | odd | 10 |